Answer
given,
constant velocity of the cart (v)= 30 m/s
initial vertical velocity of missile (v₁)= 40 m/s
At maximum height of vertical velocity of the object is zero
a) maximum height of the rocket
using equation of motion
[tex]v_2^2 = v_1^2 + 2 a y[/tex]
[tex]y = \dfrac{v_2^2-v_1^2}{2 g}[/tex]
[tex]y =\dfrac{0^2- 40^2}{- 2\times 9.8}[/tex]
y = 81.63 m
b) calculation of time of flight
[tex](y -y_0) = v_1 t - \dfrac{1}{2}gt^2[/tex]
[tex]0 =v_1 t - \dfrac{1}{2}gt^2[/tex]
[tex]t = \dfrac{2 \times v_1}{g}[/tex]
[tex]t = \dfrac{2 \times 40}{9.8}[/tex]
t = 8.163 s
distance travel by the cart = v x t
= 30 x 8.163
= 244.89 ≈ 245 m
c) rocket will land into the cart because there is no horizontal acceleration so, velocity remain same.
