You have both the initial velocity and the acceleration pointing downward. By the wording of the question, you have chosen "downward" as negative as shown by a(t) < 0; so the initial velocity is also downward as it's a negative value. So V = - U - AT = - 100 - 32*T and for every second of its descent it would be 32 fps faster going downward. It would not slow down and it would crash.
But what I think you meant is:
V = U - AT = 100 - 32*T; so it would come to a safe touchdown near zero vertical speed in T = 100/32 = 3.125 seconds. ANS.
Here I set "downward" as positive by U > 0 so that A < 0, negative 32, means deceleration as it's working in the opposite direction to U.
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They would crash burn and die. Here's why.
You have both the initial velocity and the acceleration pointing downward. By the wording of the question, you have chosen "downward" as negative as shown by a(t) < 0; so the initial velocity is also downward as it's a negative value. So V = - U - AT = - 100 - 32*T and for every second of its descent it would be 32 fps faster going downward. It would not slow down and it would crash.
But what I think you meant is:
V = U - AT = 100 - 32*T; so it would come to a safe touchdown near zero vertical speed in T = 100/32 = 3.125 seconds. ANS.
Here I set "downward" as positive by U > 0 so that A < 0, negative 32, means deceleration as it's working in the opposite direction to U.