Speed of a Motorcycle: Loading a Bike

The Physics Factbook™
Edited by Glenn Elert -- Written by his students
An educational, Fair Use website

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:

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 = y_o + v_ot + ½&nsp;at²
y_max = 0 m + (0 m/s) t + ½&nsp;at²
y_max = ½&nsp;at²
y_max = ½&nsp;(9.81 m/s²)(1.14 s)²
y_max = 6.37 m

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

v_y² = v_o² + 2as
v_y² = (0 m/s)² + 2ay_max
v_y² = 2ay_max
v_y = (2ay_max)^½&nsp;
v_y = (2(9.81 m/s²)(6.37 m))^½&nsp;
v_y = 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° = (opposite) / (adjacent)
tan 45° = v_y / v_x
v_x = v_y / tan 45°
v_x = (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 = v_x² + v_y²
v = (v_x² + v_y²)^½
v = ((11.18 m/s)² + (11.18 m/s)²)^½
v = 15.81 m/s at 45°

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

Manuel Caban -- 2005

Physics on Film pages in The Physics Factbook™ for 2005

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