To solve these problems, we can use the principles of motion and the equations of kinematics.
1) Stone Problem:
i) To find the time it took for the first stone to reach the ground, we can use the equation of motion:
y = (1/2) * g * t^2
The initial velocity of the first stone is 0 m/s since it was dropped. The acceleration due to gravity, g, is approximately 9.8 m/s^2. To find the time, we can rearrange the equation:
t^2 = 2y / g
Plug in the value for y, which is the height of the building.
ii) To find the height of the building, we can use the equation:
y = v0 * t + (1/2) * g * t^2
The initial velocity of the second stone is 25 m/s, and the acceleration due to gravity, g, is approximately 9.8 m/s^2. We need to find the time, which can be rearranged:
y = v0 * t + (1/2) * g * t^2
Let y be the height of the building, t the time it takes to reach the ground, and v0 the initial velocity of the second stone. Rearrange the equation to solve for y.
iii) To find the speeds of the two stones just before they hit the ground, we can use the equation:
vf = v0 + gt
Plug in the values for v0 and t to find the final velocity, vf, for each stone.
2) Jet Fighter Problem:
i) To find the time it takes for the tank to hit the ground, we can use the equation:
y = v0t + (1/2)gt^2
The initial vertical velocity, v0, of the tank is 0 m/s since it was released horizontally, and the acceleration due to gravity, g, is approximately 9.8 m/s^2. Solve for t to find the time it takes.
ii) To find the speed of the tank just before it hits the ground, we can use the equation:
vf = v0 + gt
Plug in the values for v0 and t to find the final velocity, vf, of the tank.
iii) To find the horizontal distance traveled by the tank, we can use the equation:
d = v0t
Plug in the values for v0 and t to find the horizontal distance, d, traveled by the tank.