Question

A cart is moving horizontally along a straight line with constant speed of 20 m/s.A projectile is to be fired from the moving cart so that it returns to the same cart after the cart has moved 60 m.The speed with which the projectile must be fired with respect to the cart is
1) 5 m/s
2) 10 m/s
3) 15 m/s
4) 20 m/s

Answer 1

1. A cart is moving horizontally along a straight line with constant speed of $20\,\mathrm{m/s}$. A projectile is to be fired from the moving cart so that it returns to the same cart after the cart has moved $60\,\mathrm{m}$. The speed with which the projectile must be fired with respect to the cart is:

1) $5\,\mathrm{m/s}$;

2) $10\,\mathrm{m/s}$;

3) $15\,\mathrm{m/s}$;

4) $20\,\mathrm{m/s}$.

Taking into account the reversing movement (down to the earth), one can express the total time of flight of the projectile:

$$t = \frac{2 v_1}{g}.$$

Let equate the time expressions.

$$\frac{l}{v} = \frac{2 v_1}{g}.$$

We can find the initial velocity of the projectile:

$$v_1 = \frac{g l}{2 v}.$$

Let check the dimension.

$$\left[ v_1 \right] = \frac{\frac{m}{s^2} \cdot m}{\frac{m}{s}} = \frac{m}{s}.$$

Let evaluate the quantity.

$$v_1 = \frac{10 \cdot 60}{2 \cdot 20} = 15 \left(\frac{m}{s}\right).$$

Answer: 3.