From the top of a tower is an object with mass 25 kg is lowered at constant speed, 4 m / s with a rope to the ground. After 10 seconds of the rope breaks, and the object falls freely. From the moment (the rope breaks) there are 12 seconds to those standing on top of the tower and put the object down hear the sound of the shot towards the ground.

The speed of sound is 334 m / s
Need help setting up the equation to determine the height of the tower.

To determine the height of the tower, we can consider two separate scenarios: before the rope breaks and after the rope breaks.

1. Before the rope breaks:
The object is lowered at a constant speed of 4 m/s for 10 seconds. Therefore, the distance covered during this time can be calculated by multiplying the speed by the time: distance = speed × time = 4 m/s × 10 s = 40 m.

2. After the rope breaks:
When the rope breaks, the object falls freely due to gravity. During the 12 seconds from the time the rope breaks to when the sound is heard at the top of the tower, the object is accelerating downward at the rate of 9.8 m/s² (acceleration due to gravity).

We can use the equation of motion for free fall:

distance = initial velocity × time + (1/2) × acceleration × time²

In this case, the initial velocity is 0 m/s since the object is at rest when the rope breaks. The distance is the entire height of the tower (which we want to find), the acceleration is -9.8 m/s² (negative sign because it is in the opposite direction to the distance), and the time is 12 seconds.

distance = 0 × 12 + (1/2) × (-9.8 m/s²) × (12 s)²
distance = -4.9 m/s² × 144 s²
distance = -4.9 × 144 m

The negative sign indicates that the object is moving downward.

Now, to find the total height of the tower, we can add the distance covered before the rope broke (40 m) to the distance covered after the rope broke (-4.9 × 144 m), and take the absolute value since height cannot be negative:

total height = |40 m + (-4.9 × 144 m)|

Finally, to convert this distance into time, we need to divide it by the speed of sound, which is 334 m/s:

time = total height / speed of sound
time = |40 m + (-4.9 × 144 m)| / 334 m/s

This equation will help us determine the height of the tower.