Question

Calculate the force a 70.0 , {kg} high jumper must exert on the ground to produce an upward acceleration 4.00 times the acceleration due to gravity. Explicitly show how you follow the steps in the ProblemSolving Strategy for Newton’s laws of motion.

What force must the high jumper exert?
a) 280 , {N}
b) 490 , {N}
c) 700 , {N}
d) 980 , {N}

Answer 1

Using Newton's second law, the high jumper must exert a force of 3430 N on the ground to achieve an upward acceleration four times that of gravity.

Step-by-step explanation:

To determine the force the high jumper must exert on the ground, we use Newton's second law of motion, which states that force is equal to mass times acceleration (F = ma). In this case, the desired acceleration is four times the acceleration due to gravity (4g), where g = 9.8 m/s2. The mass (m) of the high jumper is given as 70.0 kg. Therefore, we calculate the force (F) as follows:

F = m × (a + g)

Since a = 4g, we can write:

F = m × (4g + g) = 70.0 kg × (4 × 9.8 m/s2 + 9.8 m/s2)

Now, let's calculate this:

F = 70.0 kg × (39.2 m/s2 + 9.8 m/s2) = 70.0 kg × 49.0 m/s2 = 3430 N

This means the force exerted by the high-jumper on the ground is 3430 N, and the reaction force from the ground will be of the same magnitude but directed upwards, propelling the jumper into the air. This is consistent with Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.