Question

Jules Verne in 1865 proposed sending people to the Moon by firing a space
capsule from a cannon. The proposed length of the cannon was 220m. If
launch velocity is 11kmps, what would have been the unrealistically large
acceleration during launch?

Answer 1

Answer: The unrealistically large acceleration produced during the launch will be 2.75 X $10^5$ $\frac{m}{s^2}$ .

Explanation:

In order to solve this problem, we will have to use Kinematic equation.

Given in the question,

Length of cannon = S = 220 m.

Initial velocity = $v_i$ = 0 $\frac{m}{s}$

Final Velocity = $v_f$ = 11 $\frac{km}{s}$ = 11000  $\frac{m}{s}$

Let a be the unrealistically large acceleration produced during the launch.

∴ Kinematic equation says,

$v_f^2$  =  $v_i^2$ + 2 aS

2 aS = $v_f^2$  -  $v_i^2$

∴ a = $\frac{v_f^2}{2S}$

a = $\frac{11000^2}{2 X 220}$

a = 2.75 X $10^5$ $\frac{m}{s^2}$ .

Hence, The unrealistically large acceleration produced during the launch will be 2.75 X $10^5$ $\frac{m}{s^2}$ .

Answer 2

Given :

The length of the canon = 220m

Launch velocity of the capsule = 11km/s

To Find :

The acceleration that should be given to capsule at the time of launch = ?

Solution :

• From equations of motion, we have   $v^{2}-u^{2}=2aS$

• By substituting the given values in the equation

          $v^{2}-u^{2}=2aS$

          $v^{2}=2aS$

          $a=\frac{v^{2}}{2S}$

          $a=\frac{11000^{2}}{2\times 220}$

          $a=2.75\times 10^{5}m/s^{2}$

The unreastically large acceleration that should be given to capsule at the time of launch is 2.75×10⁵ m/s².