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## Introduction

This is a mechanics problem that a physics student should be able to solve.

In the clip "Loading a Bike", a man rides his motorcycle off a 45° ramp into a white van.

The following can be determined when analyzing the clip:

1. Maximum Height
2. Take Off Speed
3. Horizontal Distance

## 1. Maximum Height

Find the hang time by counting the frames from when the motorcycle leaves the ramp until it enters the van using Windows Media Player Classic. The frame rate can be found by locating it at the bottom of Windows Media Player Classic.

hang time = 57 frames
frame rate = 25 frames per second

To calculate the hang time in seconds, divide the hang time by the frame rate.

time = (hang time)/(frame rate)
time = (57 frames)/(25 frames per second)
time = 2.28 seconds

Now assuming that the incline is 45° and the take off and landing are the same height, the maximum height can be found. Since we are calculating the maximum height, the time is halved.

s = yo + vot + ½&nsp;at2
ymax = 0 m + (0 m/s) t + ½&nsp;at2
ymax = ½&nsp;at2
ymax = ½&nsp;(9.81 m/s2)(1.14 s)2
ymax = 6.37 m

## 2. Take Off Speed

• To find the take off speed, the vertical and horizontal speeds must first be found. First calculate the vertical speed:

vy2 = vo2 + 2as
vy2 = (0 m/s)2 + 2aymax
vy2 = 2aymax
vy = (2aymax)½&nsp;
vy = (2(9.81 m/s2)(6.37 m))½&nsp;
vy = 11.18 m/s

• Since we know/ have assumed the incline to be 45°, trigonometry can be used to find the horizontal speed and the takeoff speed.

tan 45° = vy/vx
vx = vy/tan 45°
vx = (11.18 m/s)/(1) = 11.18 m/s

• Now that we have horizontal and vertical velocity components the Pythagorean theorem can be used to solve for takeoff speed.

c2 = a2 + b2
v2 = vx2 + vy2
v = (vx2 + vy2)½
v = ((11.18 m/s)2 + (11.18 m/s)2)½
v = 15.81 m/s at 45°

## 3. Horizontal Distance

• Vertical and horizontal acceleration and velocities are independent of each other.
• Using the horizontal speed calculated in the previous part, the horizontal distance can be found.

s = vxt
s = (11.18 m/s)(2.28 s)
s = 25.49 m

Manuel Caban -- 2005

Physics on Film
1. Feature Films
2. One Reelers
3. Short Video Clips