The height in meters of a projectile is modeled the function h(t)= -5t^2+25, where t is the time in seconds. a) Find the point when the object hits the ground. b) Find the average rate of change from the point when the projectile is launched to the point in which it hits the ground. c) Estimate the object’s speed at the point of impact.

Question

The height in meters of a projectile is modeled the function h(t)= -5t^2+25, where t is the time in seconds. a) Find the point when the object hits the ground.  b) Find the average rate of change from the point when the projectile is launched to the point in which it hits the ground. c) Estimate the object’s speed at the point of impact.

irishboy123 · Answer

Assumption - from the wording this problem does not include the use of calculus.  If that is correct:

a)  it hits the ground when h(t) = 0.  so set -5t^2+25 to zero and solve for t.

b) "average rate of change " of what?  if this is asking for speed, you know the distance it travelled and the time it took to hit the ground so you can work from there.

c) you know the average speed over the fall, and you can assume that its initial speed is zero.  you can make a guess at the final speed (which is in fact the real final speed, in this case) by assuming that speed increases linearly from zero to X where the average of zero and X is your answer to b).