Answer to Question #349438 in Physics for sada

Question

A body is projected downward at an angle of 30° with the horizontal from the

top of a building 170 m high.

Its initial speed is 40 m/s. (a) How long will it

take before striking the ground? (b) How far from the foot of the building will it

strike? (c) At what angle with the horizontal will it strike?

Answer 1

$$x(t)=v_0\cos\theta*t\\ =40*\cos30^\circ*t=34.6t\;\rm m$$

$$y(t)=y_0-v_0\sin\theta*t-g*t^2/2\\ =170-40*\sin30^\circ*t-9.8*t^2/2\\ =170-20t-4.9t^2\;\rm m$$

(a) at the ground

$$y(t)=170-20t-4.9t^2=0$$

So

$$t=4.2\:\rm s$$

(b)

$$x(t)=34.6*4.2=145\:\rm m$$

(c)

$$v_x=v_0\cos\theta=34.6\:{\rm m/s}\\ v_y=v_0\sin\theta+gt=20+9.8*4.2=61\:\rm m/s$$

$$\theta=\tan^{-1}\frac{v_y}{v_x}=\tan^{-1}\frac{61}{34.6}=60^\circ$$