Question

A missile is launched on earth with the initial velocity of 100ms-1 at an elevation of 30 degrees.calculate

1 greatest height attained

2 horizontal range

3 time of fright

4 velocity of a missile at time 8 second

Answer 1

1.

$$H_{\max}=\frac{v_0^2\sin^2\theta}{2g}$$

$$H_{\max}=\frac{100^2\sin^230^\circ}{2*9.8}=128\:\rm m$$

2.

$$R=\frac{v_0^2\sin2\theta}{g}$$

$$R=\frac{100^2\sin60^\circ}{9.8}=884\:\rm m$$

3.

$$t=\frac{2v_0\sin\theta}{g}$$

$$t=\frac{2*100\sin30^\circ}{9.8}=10.2\:\rm s$$

4.

$$v=\sqrt{(v_0\cos\theta)^2+(v_0\sin\theta-gt)^2}$$

$$v=\sqrt{(100\cos30^\circ)^2+(100\sin30^\circ-9.8*8.0)^2}=91\:\rm m/s$$