A stone is dropped from the upper observation deck of a tower, 650 m above the ground. (Assume g = 9.8 m/s2.) (a) Find the distance (in meters) of the stone above ground level at time t.

Question

A stone is dropped from the upper observation deck of a tower, 650 m above the ground. (Assume g = 9.8 m/s².)

(a) Find the distance (in meters) of the stone above ground level at time t.

(b) How long does it take the stone to reach the ground? (Round your answer to two decimal places.)

(c) With what velocity does it strike the ground? (Round your answer to one decimal place.)

(d) If the stone is thrown downward with a speed of 3 m/s, how long does it take to reach the ground? (Round your answer to two decimal places.)

Answer 1

(a) d(t) = 0.5 (-9.8) t² + v(0) t + d(0) = (-4.9)t² + 0t + 650 = -4.9t² + 650

(b) i.e. What is time 't' when d = 0? Substituting in the above equation.

d = -4.9t² + 650 = 0

t² = (-650) / (-4.9) = 132.653

t = 11.52 seconds

(c) i.e. What is the velocity when t = 11.52 seconds?

v(t) = v(0) + gt v(11.52) = 0 + (9.8)(11.52) = 112.9 m/s

(d) v(0) = -3 m/s ; Velocity is negative because stone is being thrown downward.

d(t) = 0 = (-4.9)t² + v(0) t + d(0) = (-4.9)t² -3t + 650

Using the quadratic formula to solve to t, gives t = -11.83 , 11.22

We can disregard the negative solution, giving t = 11.22 seconds.

Note, when the stone is thrown towards the ground, it will reach the ground sooner than if being dropped. i.e. the time given in answer (d) should be a little bit less than that given in answer (b).

Answer 2

(a) y = 650 - 4.9t²_.

(b) At ground level y = 650 - 4.9t² = 0; t = √(650/4.9) = 11.52 s

(c) v = - gt = - 9.8 m/s²·11.52 = - 112.9 m/s.

(d) y = 650 - 3t - 4.9t² = 0; t = 11.22 s