A rock is dropped from a bridge that is 45 m above the water. It falls directly into a model boat, moving with constant velocity, that is 12 m from the point of impact when the key is released. What is the speed of the boat?

Question

A rock is dropped from a bridge that is 45 m above the water. It falls directly into a model boat, moving with constant velocity, that is 12 m from the point of impact when the key is released. What is the speed of the boat?

Answer 1

time to drop 45 m

45 = (1/2)(9.81)t^2
t = 3.03 seconds

12 m/3.03 s = 3.96 m/s

Answer 2

To find the speed of the boat, we need to use the principles of projectile motion.

Step 1: Determine the time it takes for the rock to fall from the bridge to the point of impact on the boat.

Using the formula for free fall:
𝑑 = (1/2)𝑔𝑡^2

where 𝑑 is the distance fallen, 𝑔 is the acceleration due to gravity, and 𝑡 is the time taken, we can rearrange the formula to solve for 𝑡:

𝑡 = √(2𝑑/𝑔)

Plugging in the values:
𝑡 = √(2*45/9.8)
𝑡 ≈ 3.02 seconds

Step 2: Calculate the horizontal distance the boat moves during that time.

Since the boat is moving with constant velocity, we can use the formula:
𝑑 = 𝑣𝑡
where 𝑑 is the distance, 𝑣 is the velocity, and 𝑡 is the time.

Plugging in the values:
12 = 𝑣 * 3.02
𝑣 ≈ 3.98 m/s

Therefore, the speed of the boat is approximately 3.98 meters per second.