Question

(a) A daredevil is attempting to jump his motorcycle over a line of buses parked end to end by driving up a 32º ramp at a speed of 40.0 m/s (144 km/h). How many buses can he clear if the top of the takeoff ramp is at the same height as the bus tops and the buses are 20.0 m long? (b) Discuss what your answer implies about the margin of error in this act—that is, consider how much greater the range is than the horizontal distance he must travel to miss the end of the last bus. (Neglect air resistance.)(a) How many buses can he clear if the top of the takeoff ramp is at the same height as the bus tops and the buses are 20.0 m long?

a) 2
b) 3
c) 4
d) 5

Answer 1

The daredevil can clear approximately 9 buses if the top of the takeoff ramp is at the same height as the bus tops and the buses are 20.0 m long.

Step-by-step explanation:

To determine how many buses the daredevil can clear, we need to calculate the horizontal distance he can travel based on his speed and the angle of the ramp. Using the equation x = v*cos(theta)*t, where x is the horizontal distance, v is the speed, theta is the angle, and t is the time, we can plug in the values and solve for x. In this case, v = 40.0 m/s and theta = 32°.

First, convert the angle from degrees to radians: theta_rad = (32° * pi/180) = 0.558003 rad. Next, we can calculate the horizontal distance using the equation:

x = (40.0 m/s) * cos(0.558003 rad) * t

Since the time t is not given, we need to find it using the equation:

t = 2v*sin(theta) / g, where g is the acceleration due to gravity. The angle of the ramp is 32°, so we can calculate t as follows:

t = (2*40.0 m/s * sin(0.558003 rad)) / 9.8 m/s² = 4.48 s.

Finally, we can substitute the value of t back into the equation to find the horizontal distance:

x = (40.0 m/s) * cos(0.558003 rad) * 4.48 s = 173.31 m.

Therefore, the daredevil can clear approximately 9 buses, each with a length of 20.0 m, since 9*20.0 m = 180.0 m is greater than the horizontal distance he can travel.