Question

Timothy, the daredevil, is going to jump his car over the ravine. He starts on the edge of the canyon that is 367 feet tall and ends on the other side, which is 22 feet tall. He calculated that he needs to drive off a 32 degree ramp at exactly 72 mph to make it to the other side. How big was the ravine? (aka how far did he travel in the x-direction to make the jump (in meters)?

Answer 1

1 feet =0.3048 m

1 mph =0.44704 m/s

Initial Horizontal and vertical components of velocities are

V_ox=(72*0.44704)Cos32 = 27.296 m/s

V_oy =(72*0.44704)Sin32 = 17.0564 m/s

From Kinematic equation

Y=Y_O+V_oyt -(1/2)gt²

(22*0.3048) = (367*0.3048)+(17.0564)t-(1/2)(9.81)t²

4.905t²-17.0564t-105.156=0

t=6.68454 s

Horizontal distance

D=V_oxt =(27.296)(6.68454)

D=182.46 m