Question

Problem 12:

A cart is moving horizontally along a straight line with constant speed 30 m/s. A projectile is to be fired from the moving cart in such a way that it will return to the cart after the cart has moved 80m. At what speed (relative to the cart) and at what angle (to the horizontal) must the projectile be fired?

NOTE: remember that to calculate the speed of the projectile respect to the cart, we need to subtract the velocity of the cart from the calculated velocity of the projectile.

Answer 1

PROBLEM 12

it is very clear from intuition that the projectile must be fired vertically,

the flight time can be found as

d = vt

t = d / v

t = 80 / 30

t = 2.666 seconds

now, we can find the velocity of launch using kinematics with flight time as found above

y = v_ot - 1/2gt²

as initial and final position of projectile are same ( on the cart) , y = 0

so,

0 = v_ot - 1/2gt²

v_o * 2.666 = 4.9 * 2.666²

v_o = 13.1 m/s

so,

projectile must be fired at initial speed of 13.1 m/s at an angle of 90 degree