Two carts connected to each other (Fig. 7.16) with a horizontal inextensible bar, move with a constant velocity \(v_{0}=10.0 \mathrm{~m} / \mathrm{s}\) on straight track parallel to the ground. Each cart consists of a horizontal platform of mass \(m=150 \mathrm{~kg}\) and four wheels of negligible mass. On the track of the first cart there is a small box of mass \(M=30.0 \mathrm{~kg}\). During the motion, the box is thrown (almost instantaneously) towards the second cart with a velocity of magnitude \(v_{f}=6.00 \mathrm{~m} / \mathrm{s}\) and an elevation angle \(\alpha=30.0^{\circ}\) with respect to the cart, that is moving with speed \(v_{0}\). Calculate:

1. the velocity \(v_{1}\) of the two carts when the box is on flight;

2. the distance \(l\) from the launch point at which the box falls onto the second cart with respect to the carts reference frame;

3. the average tension \(T\) applied to the bar connecting the two trolleys during the launch of the box, if the launching time can be considered to be \(\Delta t=0.100 \mathrm{~s}\) and the launching force to be constant.

FL M m Fig. 7.16 On the left: figure for Exercise 7.1. On the right: figure for Exercise 7.2