Projectile Motion Analysis: Mass, Angle, and Speed Effects

This physics assignment delves into the principles of projectile motion, examining the influence of various factors on the trajectory of objects. The assignment explores how mass affects the horizontal distance (range) and vertical distance (maximum height) of projectiles, demonstrating through simulations that mass has no impact when initial speed and launch angle are constant. It then investigates the effects of different launch angles (30, 45, and 65 degrees) on range and flight time, revealing that a 45-degree angle maximizes range and that a higher launch angle leads to longer flight times. Finally, it analyzes the impact of doubling the initial speed on range, maximum height, and flight time, highlighting the proportional and quadratic relationships. The assignment concludes with a problem involving hitting a target at a specific horizontal distance and height, requiring the calculation of launch angles.

PROJECTILE MOTION
Assume no air resistance.
Please enter the answer you expect before actually running the simulation
1.
a) Do you EXPECT the horizontal distance (Range) an object flies to depend on its mass?
Expectation: No
Explain your reasoning.
Mass of an object no effect on the horizontal distance, it’s the initial speed and direction of
movement that affects the horizontal distance.
Simulation: No
A cannonball was used to demonstrate this, at the constant initial speed and launch angle of
30m/s and 40 degrees respectively and a variable mass. It was observed that the cannonball
flies to the same horizontal distance irrespective of the mass chosen. The horizontal distance
for the simulation was 92m for 1kg, 20kg and 30 kg mass.
b) Do you EXPECT a Buick car to fly longer or shorter distance than a golf ball given the
same initial speeds and launch angles?
Expectation: Both Buick car and golf ball will fly the same distance.
Explain your reasoning.
As long the initial speed and launch angle are kept, the two will fly the same distance. The
two objects differ by mass, and mass does not affect the distance.
Expectation: same distance
In the simulation, Buick car flies to a distance of 92m, when its initial speed and launching
angle was set to 30m/s and 40 degrees respectively, the same was observed golf ball. The
mass does not affect the distance an object travel.
2.
a) Do you EXPECT the vertical distance an object flies (Maximum Height) to be dependent on
its mass?
Expectation: No
Mass of an object no effect on the vertical distance, it’s the initial speed and direction of
movement that affects the horizontal distance
Simulation: No
Dr. Howard – 2019 Fall

A car with a mass of 2000kg flies to a maximum height of 20.95m. A with a different mass
of 4000kg flies to the same maximum height of 20.95m. Both are subjected to same initial
speed and launching angle. That shows that mass has no effect on the maximum height an
object fly.
b) Do you EXPECT a Buick car to climb up higher or lower than a golf ball given the same
initial speeds and launch angles?
Expectation: same
Since the two objects are subjected to the same initial speeds and launch angles, the vertical
distances are expected to be the same, the difference in their masses does not affect the
vertical height they fly.
Simulation: Same
A car with a mass of 2000kg flies to a maximum height of 20.95m, a golf ball with a mass
of 0.05kg flies to the maximum height of 20.95m. Both objects are launched at the same
initial speed and angle of 30m/s and forty degrees respectively. The two objects flies the
same vertical height despite the difference in mass.
3. Three objects are being shot with the same speeds but with the different launch angles of 65%,
45%, and 30%. Which object do you EXPECT to fly longer horizontal distance (Range)? Rank
the results with the numbers 1, 2, and 3. (1 for the winner)
Expectation: 65 deg: 3 45 deg: 1 30 deg: 2
The ball launched at 65 degrees will not fall far from point of trajectory as its flies to a
longer vertical distance, thus its flies a shorter horizontal distance. A ball launched at 45
degrees will have fairly enough angle to travel the farthest horizontal distance possible.
Lastly the ball launched at 30 degrees will have lower angle to fly longer horizontal distance
compared to the ball launched at 45 degrees.
Simulation: 65 deg: 3 45 deg: 1 30 deg: 2
A golf ball launched at an initial speed of 30 m/s at different launching angles are simulated,
the ball launched at angle of 30 degrees flied to a horizontal distance of 90 meters, ball
launched at 45 degrees flied to a horizontal speed of 93.91 meters and lastly a ball launched
at an angle of 65 degrees flied to an horizontal distance of 71.7 meters.
4. Three objects are being shot with the same speeds but with the different launch angles of 65%,
45%, and 30%. Which object do you EXPECT to stay in the air longer? Rank the results with
the numbers 1, 2, and 3. (1 for the winner)
Dr. Howard – 2019 Fall

Expectation: 65 deg: 1 45 deg: 2 30 deg: 3
The object launched at angle of 65 degrees stays the longest time in the air, since it fly the
maximum vertical height, an object launched at 45 degrees fly comes second in terms of
height it travels, and finally the one launched at 30 degrees. An object flying to a shortest
vertical distance takes the shortest time in the air
Simulation: 65 deg: 1 45 deg: 2 30 deg: 3
A golf ball was launched at 65, 45 and 30 degrees, at a constant speed of 30m/s. The ball
launched at 65degrees takes 2.77seconds to fly to the maximum height, ball launched at 45
degrees takes 2.16 seconds to fly to the maximum height, and one launched at 30 degrees
takes 1.53 seconds to fly to the maximum height. This shows one launched at 65 degrees
takes the longest time in air.
5. If the initial speed is doubled, given the same launch angle, how that would affect:
Range:
Expectation: Quadrable
Doubling initial speed means a reduction in maximum height and time it takes in air, thus
range is quadrable, the same can be deduced from linear equations of motions
Simulation: triple
At initial speed of 15m/s the range is 25.25 and at initial speed of 30m/s the range is 93.91
this almost a quadrable
Max Height:
Expectation: Triple
when the initial speed is doubled, the height it goes is expected to goes more than twice the
initial height from linear equations of motion
Simulation: triple
At 15 m/s the maximum height is 7.73 meters, at initial speed of 30m/s the maximum is
24.94 meters, which nearly triple the initial
Flight Time:
Expectation: Double
Explain your reasoning.
Since the speed is doubled it is expected that time it takes to fly will be doubled
Simulation: Double
Dr. Howard – 2019 Fall

The ball took 2.34 seconds to fly with an initial speed of 15m/s, the same ball took 4.42
seconds to fly, with an initial speed of 15m/s. thus the double time.
6. Move the target at the horizontal distance 78 m away and the height of 90 m. Use a stretchable
and movable ruler shown to achieve that. Try to shoot with a piano to hit a target with the initial
speed of 50 m/s. Record the EXPECTED and SIMULATED launch angles.
a)
Expected Angle: ____________
Simulated Angle: ____________
b) There are two possible solutions to 6a). Provide the other possible solution below
Dr. Howard – 2019 Fall