Find the speed, in m/s, of the large block before the collision.

Question

A large block of mass 3.80 kg slides on a frictionless table and collides head-on with a small block of mass 2.50 kg. After the collision both blocks move in the same direction as the original motion of the large block, and fall off the edge of the table. The small block hits the floor at a point 2.16 meters horizontally from the edge of the table, while the large block hits the floor at a point 1.32 meters horizontally from the edge of the table. The top of the table is 1.10 m above the floor. Find the speed, in m/s, of the large block before the collision.

Answer 1

This is a multistep question that builds on multiple prior subjects.

You are initially given a scenario of a collision resulting in the two blocks falling off a table at different speeds, and are given how far the blocks fall from the table. To get to the answer, the speed of the large block before the collision, you need to work backwards. Start with the top of the table, and remember that objects like this will have the same acceleration downward as an object dropped from this height. Use this to find out how long they were in the air before hitting the ground. We'll call that T for time.

Y = 0.5aT² -> T = root(2Y/a)

Y = 1.10 m, a = 9.8 m/s²

Then, using the distance from the edge of the table and your kinematics equation at net 0 acceleration, you can figure out the speeds of the big block, call it M₁ and v₁, and the small block, M₂ and v₂, based on their distances d₁ and d₂ and the time calculated before, T.

M₁: d₁ = v₁*T -> v₁ = d₁/T = d₁/root(2Y/a)

M₂: d₂ = v₂*T -> v₂ = d₂/T = d₂/root(2Y/a)

Now that you have v1 and v2, you know that momentum is conserved before and after collisions. The initial velocity of the small block is 0, and the answer you are after is the initial velocity of M1, let's call it v₀.

M₁ * v₀ = M₁v₁ + M₂v₂ -> v₀ = (M₁v₁ + M₂v₂) / M₁

Fill in the values for M₁ and M₂ as given in the problem, and v₁ and v₂ as derived above. When I plug in the numbers, I get a pre-collision speed of 5.8 m/s.