A coin is pushed from the edge of a laboratory bench with a horizontal velocity of 15.0 ms-1. If the height of the bench from the floor is 1.5m, calculate t...

A coin is pushed from the edge of a laboratory bench with a horizontal velocity of 15.0 ms^-1. If the height of the bench from the floor is 1.5m, calculate the distance from the foot of the bench to the point of impact with the floor [g = 10ms^-2]

Answer Details

We can solve this problem using kinematic equations of motion. Since the motion is projectile motion, we can break it into two components, horizontal and vertical. In the horizontal direction, there is no acceleration, so the velocity remains constant throughout the motion. In the vertical direction, the coin is moving upward against the force of gravity, which causes it to slow down, then come to rest at the highest point before falling downward. The time taken to reach the highest point can be calculated using the vertical component of the initial velocity and acceleration due to gravity. Using the equation: v = u + at where: v = final velocity = 0 (at the highest point) u = initial velocity = 0 a = acceleration due to gravity = 10 ms^-2 t = time taken to reach the highest point Solving for t, we get: t = u/a = 15.0/10 = 1.5s The maximum height reached by the coin can be calculated using the equation: s = ut + 0.5at^2 where: s = maximum height reached u = initial vertical velocity = 0 a = acceleration due to gravity = 10 ms^-2 t = time taken to reach the highest point = 1.5s Solving for s, we get: s = 0 + 0.5 x 10 x (1.5)^2 = 11.25m Now, the coin falls from the maximum height and hits the floor. The time taken to fall from the maximum height can be calculated using the equation: s = ut + 0.5at^2 where: s = height of the bench = 1.5m u = initial vertical velocity = 0 a = acceleration due to gravity = 10 ms^-2 t = time taken to fall from maximum height Solving for t, we get: 1.5 = 0 + 0.5 x 10 x t^2 t^2 = 0.3 t = sqrt(0.3) = 0.55s (ignoring the negative root) Now, we can calculate the horizontal distance traveled by the coin during the time it was in the air using the equation: s = ut + 0.5at^2 where: s = horizontal distance traveled u = initial horizontal velocity = 15.0ms^-1 a = acceleration in horizontal direction = 0 (no acceleration) t = time taken to fall from maximum height = 0.55s Solving for s, we get: s = 15.0 x 0.55 = 8.25m Therefore, the distance from the foot of the bench to the point of impact with the floor is approximately 8.25m. Answer: 8.22m (rounding off to two decimal places)