Final answer:
Tyrone's final speed after experiencing a resistive force of 815 N for 1.09 seconds would be 4.52 m/s. This calculation uses the impulse-momentum theorem and takes into account the mass of the player and his initial velocity.
Step-by-step explanation:
To calculate Tyrone's final speed after experiencing a resistive force, we must first determine the change in momentum (impulse) caused by the force over the time period and then apply this to find the new velocity.
We begin by using the impulse-momentum theorem which states that the impulse acting on an object is equal to the change in momentum of the object:
Impulse = Force × Time = Change in momentum
Given:
Resistive Force (F) = 815 N
Time (t) = 1.09 s
Initial Velocity (vi) = 6.99 m/s
Mass (m) = 77.2 kg
We can calculate the impulse:
Impulse = F × t
Impulse = 815 N × 1.09 s
Impulse = 888.35 kg·m/s
The change in momentum is in the direction opposite to the velocity since it's a resistive force, and hence will be subtracted from the initial momentum to find the final momentum (pf).
The initial momentum (pi) is given by:
pi = m × vi
pi = 77.2 kg × 6.99 m/s
pi = 539.608 kg·m/s
We subtract the impulse to find the final momentum (pf):
pf = pi - Impulse
pf = 539.608 kg·m/s - 888.35 kg·m/s
pf = -348.742 kg·m/s
Since momentum is mass times velocity, we can find the final speed (vf) by dividing the final momentum by the mass:
vf = pf / m
vf = -348.742 kg·m/s / 77.2 kg
vf = -4.52 m/s
The negative sign means that Tyrone would be moving in the opposite direction after the collision. However, since the question asks for a positive number, we report the magnitude of the final speed which is:
Final Speed (vf) = 4.52 m/s