Question

An aircraft shell is fired vertically upward with an initial velocity of 500 m/s. Find the ff:

a) maximum height it can reach

b) time taken to reach that height

Answer 1

(a) Let’s take the upwards as the positive direction. Then, we can find the maximum height from the kinematic equation:

$$v_f^2=v_i^2+2gh,$$

here, $v_f=0\ ms^{-1}$ is the final velocity of the shell at the maximum height, $v_i=500\ ms^{-1}$ is the initial velocity of the shell, $g=-9.8\ ms^{-2}$ is the acceleration due to gravity, $h$ is the height.

Then, we get:

$$h=-\dfrac{v_i^2}{2g}=-\dfrac{(500\ ms^{-1})^2}{2\cdot (-9.8\ ms^{-2})}=12.75\ km.$$

(b) We can find the time that the shell takes to reach the maximum height from the kinematic equation:

$$v_f=v_i+gt,$$ $$t=\dfrac{v_f-v_i}{g}=\dfrac{0\ ms^{-1}-500\ ms^{-1}}{-9.8\ ms^{-2}}=51\ s.$$

Answer:

(a) $h=12.75\ km.$

(b) $t=51\ s.$