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Explain Bot To find the height of the stone at 5 seconds later, we need to use the formula for displacement under constant acceleration:
Displacement = Initial Velocity * Time + 0.5 * Acceleration * Time^2
A. For the first question, we are given that the stone is thrown downward, so the initial velocity is -7 feet per second (negative because it is in the opposite direction to the positive direction of measurement). The acceleration due to gravity is -32 feet per second squared. Plugging in the values into the formula:
Displacement = -7 * 5 + 0.5 * (-32) * (5^2)
Displacement = -35 + 0.5 * (-32) * 25
Displacement = -35 - 16 * 25
Displacement = -35 - 400
Displacement = -435
Since the stone is thrown downward, the displacement is negative. Therefore, the height of the stone 5 seconds later is 435 feet below the initial height of 750 feet. We subtract 435 feet from 750 feet to get the final height:
Final Height = 750 - 435
Final Height = 315 feet
B. To find the time it takes for the stone to hit the ground, we need to set the displacement equal to zero and solve for time:
Displacement = -7 * t + 0.5 * (-32) * t^2 = 0
Simplifying the equation:
-7t - 16t^2 = 0
We can factor out a t:
t(-7 - 16t) = 0
This equation will be zero when either t = 0 or -7 - 16t = 0. Since time cannot be negative, we can solve the second equation for t:
-7 = 16t
t = -7/16
Since time cannot be negative, we discard this solution. Therefore, the only solution is t = 0. This means that the stone hits the ground at time t = 0, or immediateaneously.
C. Finally, to calculate the velocity of the stone when it hits the ground, we can use the formula:
Final Velocity = Initial Velocity + (Acceleration * Time)
Plugging in the values:
Final Velocity = -7 + (-32 * 0)
Final Velocity = -7
The negative sign indicates that the velocity is in the opposite direction of the initial velocity. Therefore, the velocity of the stone when it hits the ground is 7 feet per second, but in the opposite direction in which it was thrown.