A 100 kg sprinter pushes against the blocks with a force of -2500 N at an angle of 45° to the horizontal. What is the vertical reaction force acting on the sprinter?

To find the vertical reaction force acting on the sprinter, we first need to resolve the force applied by the sprinter into its vertical and horizontal components.

Step 1: Resolve the force into components The force applied by the sprinter has both a vertical and a horizontal component. We can find the vertical component using the formula Fv = F * sin(θ), where F is the force and θ is the angle.

Fv = -2500 N * sin(45°) = -1767.77 N

The negative sign indicates that the force is directed downwards.

Step 2: Calculate the weight of the sprinter The weight of the sprinter is given by the formula W = m * g, where m is the mass and g is the acceleration due to gravity.

W = 100 kg * 9.8 m/s² = 980 N

Step 3: Calculate the vertical reaction force The vertical reaction force (Rv) is the sum of the vertical component of the force applied by the sprinter and the weight of the sprinter.

Rv = Fv + W = -1767.77 N + 980 N = -787.77 N

The negative sign indicates that the reaction force is directed upwards. Therefore, the vertical reaction force acting on the sprinter is 787.77 N upwards.