A key falls from a bridge that is 50 m above the water. It falls directly into a model boat, moving with constant velocity, that is 18 m from the point of impact when the key is released. What is the speed of the boat ?

Question

Layla Ahmed · Accepted Answer

The speed of the boat is #"5.6 m/s"#.

The boat has to move 18 meters in the same amount of time as the key falls from a height of 50 meters, which is the key to this puzzle. Given the assumption that the key falls freely, you can state that #h = underbrace(v_0)_(color(blue)("=0)) * t + 1/2 * g * t^2# #h = 1/2 * g * t^2# Given that the boat travels at a steady speed, you could say that #v = d/t# Calculate the time it takes the key to reach the water using the first equation; this time must coincide with the time it takes the boat to position itself. #t = sqrt((2 * h)/g) = sqrt((2 * 50color(red)(cancel(color(black)("m"))))/(9.8color(red)(cancel(color(black)("m")))/"s"^2)) = "3.20 s"# This implies that the boat's speed needs to be #v = "18 m"/"3.20 s" = color(green)("5.6 m/s")#

Lily Adams · Answer

undefined The speed of the boat is 6 m/s.