Question

Let's suppose for simplicity that the gravitational field strength is g = 10 m/s^2. A projectile is shot horizontally from a height of 30 meters, quite a way up. with initial speed v_0 = 10 m/s. It strikes the side of a tower after traveling a horizontal distance of 20 meters. Show your work. (a) at what height y above the ground does the projectile strike the tower? b) what are the vertical and horizontal components v_x, v_y of its velocity when it hits the tower?

Answer 1

here,

initial horizontal speed , u0 = 10 m/s

let the time of flight be t

t = 20 /u0 = 2 s

a)

the vertical drop , h1 = 0 + 0.5 * g * t^2

h1 = 0.5 * 9.81 * 2^2

h1 = 19.6 m

the height y above the ground , y = 30 - h1 = 10.4 m

b)

the final vertical speed , vy = 0 + g * t

vy = 19.6 m/s

horizontal component of velocity , vx = u0 = 10 m/s