Old question from a previous exam. How do I solve? 4.) Car Jump (16 pts.) A toy

Question

Old question from a previous exam. How do I solve?

4.) Car Jump (16 pts.) A toy car is released from rest on a ramp h1=30cm above the ground, moving onto a launch ramp which reaches to a maximal height of h2=10cm above the ground (neglect friction and the rotational energy of the wheels). (a) What is the speed of the car once it becomes airborne? (b) If the car reaches a maximal height of 15cm above the ground during its flight, what is the inclination angle of the launch ramp with respect to the horizontal? (c) How long is the car in the air? (d) What is the horizontal flight distance?

Ans:  4.) (a) 1.98m/s (b) 30.0deg (c) 0.276s (d) 0.47m

Explanation / Answer

(a)

v = sqrt 2g( 0.30-0.10) = sqrt 2 ( 9.8) ( 0.20) = 1.98 m/s

(b)

vy = sqrt 2( 9.8) ( 0.15-0.10) = 0.9899 m/s

vx = sqrt ( 1.98)^2 - ( 0.9899)^2 = 1.71 m/s

theta = tan^-1 ( vy/vx) = tan^-1 ( 0.9899/1.71) = 30 degree

(c)

from the kinematic equaton

s= ut + 1/2 at^2

-0.10= 0.9899 t - 1/2 ( 9.8) t^2

4.98 t^2 - 0.9899 t - 0.10 = 0

solving quadratic equation

t = 0.276 s

(d)

d =vx t = 0.276s ( 1.71) = 0.47 m

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