Physics with Calc I An inquisitive physics student and mountain climber climbs a
ID: 1423554 • Letter: P
Question
Physics with Calc I
An inquisitive physics student and mountain climber climbs a 46.0 m cliff that overhangs a calm pool of water. He throws (not drops) two stones vertically downward, 1.00 s apart, and observes that they cause a single splash. The first stone has an initial speed of 1.98 m/s downward. Hint: Because the motion is only in the downward direction, choose the positive y-axis to point downward.
(a) How long after release of the first stone do the two stones hit the water?
(b) What initial velocity must the second stone have if they are to hit simultaneously?
________(downward)
(c) What is the speed of each stone at the instant the two hit the water?
first stone
________(downward)
second stone
________(downward)
(d) Draw position, velocity, and acceleration graphs.
Explanation / Answer
a) s = So + Vo*t + ½at² (let's take down as positive)
46 = 0 + 1.98*t + ½ * 9.8* t^2
4.9t² + 1.98*t - 46 = 0
solutions at t = 2.87 s
b) Then for the second stone to get there in 1 s less:
46 = Vo*1.87 + 4.9(1.87)²
Vo = 15.44 m/s
c) first: v = Vo + at = 1.98 + 9.8 * 2.87 = 30.1 m/s
second: v = 15.44 + 9.8 * 1.87 = 33.77 m/s