Final answer:
The mass of the high jumper who lands in the foam pit can be calculated using Newton's second law and the kinematic equations for motion. By determining the acceleration during deceleration in the pit and applying the net force, the jumper's mass is found to be approximately 13.94 kg.
Step-by-step explanation:
To determine the mass of the jumper, we can use Newton's second law which relates the net force to the mass of the object and the acceleration it experiences. In this case, the net force is provided, and we can calculate the acceleration from the kinematic equations that describe the motion of the jumper within the foam pit.
According to Newton's second law, the force (F) that acts on an object is equal to the mass (m) of the object multiplied by its acceleration (a): F = m × a. Since the jumper lands with a velocity (v) of -7.0 m/s and comes to rest (v = 0), we can use the following kinematic equation to calculate a, assuming the positive direction is upwards, thus making acceleration negative due to deceleration:
v² = u² + 2ad, where
- v is the final velocity (0 m/s),
- u is the initial velocity (-7.0 m/s),
- a is the acceleration, and
- d is the displacement (0.56 m).
By substituting the known values and rearranging the equation, we can solve for a.
0 = (-7.0 m/s)² + 2 × a × 0.56 m
a = 87.5 m/s²
Now, substituting the values of a and F into Newton's second law, we'll get:
1220 N = m × 87.5 m/s²
m = 1220 N / 87.5 m/s²
m = 13.94 kg
Therefore, the mass of the high jumper is approximately 13.94 kg.