Heather and Jerry are standing on a bridge 53m above a river. Heather throws a rock straight down with a speed of 12m/s . Jerry, at exactly the same instant of time, throws a rock straight up with the same speed. Ignore air resistance.
How much time elapses between the first splash and the second splash?
I tried V(f)=V(i)+at and got 98 but my prof says it wrong. I don't understand what im doing wrong
To solve this problem, we need to consider the motion of the rocks separately.
Let's start with Heather's rock. When she throws it straight down, it will accelerate due to gravity, which we can assume is 9.8 m/s² (ignoring air resistance). We know the initial velocity (V(i)) is 12 m/s and the acceleration (a) is -9.8 m/s² (negative because it is acting in the opposite direction of the initial velocity). We want to find the time it takes for the rock to hit the river.
Using the equation V(f) = V(i) + at, we can rearrange it to find t:
t = (V(f) - V(i))/a
Since the rock is thrown straight down, its final velocity (V(f)) will be the same as its initial velocity but with a negative sign (since it's moving in the opposite direction).
V(f) = -12 m/s
Plugging in these values, we get:
t = (-12 m/s - 12 m/s) / (-9.8 m/s²)
t = -24 m/s / (-9.8 m/s²)
t ≈ 2.45 seconds
So it takes approximately 2.45 seconds for Heather's rock to hit the river.
Now let's consider Jerry's rock. He throws it straight up with the same initial velocity of 12 m/s. When a rock is thrown straight up, its initial velocity is positive, but the acceleration due to gravity is acting against it, causing it to slow down before eventually falling back down. Thus, we can use the same formula to find the time it takes for Jerry's rock to reach its maximum height and fall back down.
Plugging in the values:
V(f) = 0 (since the rock reaches its maximum height and momentarily stops before falling back down)
V(i) = 12 m/s
a = -9.8 m/s²
t = (0 - 12 m/s) / (-9.8 m/s²)
t = -12 m/s / (-9.8 m/s²)
t ≈ 1.22 seconds
So it takes approximately 1.22 seconds for Jerry's rock to hit the river.
To find the time elapse between the first splash and the second splash, we subtract the time it takes for Jerry's rock to hit the river from the time it takes for Heather's rock to hit the river:
2.45 seconds - 1.22 seconds = 1.23 seconds
Therefore, the time elapse between the first splash and the second splash is approximately 1.23 seconds.