Answer to Question #266491 in Physics for Hazmy

Question

7. An anti aircraft missile is fired vertically upward from the earth’s surface with an initial

velocity of 500 m/s. Calculate:

(a) The maximum height it can reach.

(b) The time taken to reach that height.

(c) The velocity of the missile at t = 60 s.

(d) The time when it reaches the height of 10 km.

Answer 1

(a) The maximum height it can reach:

$$H_\text{max}=\frac{v^2}{2g}=12755\text{ m}.$$

(b) The time taken to reach that height:

$$t=\frac{v}{g}=51\text{ s}.$$

(c) The velocity of the missile at t = 60 s:

60 s is 9 seconds from the max. height, so, the velocity is

$$v_c=gt=9.8·9=88.2\text{ m/s}.$$

(d) The time when it reaches the height of 10 km.

$$\tau=t-\sqrt{2(y)/g},\\ \tau=51-\sqrt{2(2755)/9.8}=27.3\text{ s}.$$