A boat exerts a force of 417N pulling a water skier who is 64kg at rest. The skier speed is 15m/s. over what distance was the force exerted?
a = F/m = 417 / 64 = 6.52 m/s^2.
d = (Vf^2-Vo^2)/2a.
d = ((15)^2-0) / 13 = 17.27 m.
To find the distance over which the force was exerted, we can use the concept of work. The work done by a force on an object is equal to the force multiplied by the distance traveled in the direction of the force.
In this case, the force exerted by the boat is 417N, and we need to find the distance traveled by the water skier.
We can use the work-energy theorem to solve for the distance. The work done on the skier is equal to the change in kinetic energy.
The initial kinetic energy of the skier is zero because they are at rest. The final kinetic energy is calculated using the formula:
KE = (1/2) * mass * velocity^2
Substituting the given values:
KE = (1/2) * 64kg * (15m/s)^2
KE = 1/2 * 64kg * 225m^2/s^2
KE = 7200J
Since the initial kinetic energy is zero, the change in kinetic energy is equal to the final kinetic energy.
Therefore, the work done by the boat is also 7200J.
The work done by a force is equal to the force multiplied by the distance traveled. We can rearrange this equation to solve for the distance:
Work = Force * Distance
Distance = Work / Force
Plugging in the values:
Distance = 7200J / 417N
Distance = 17.28m
Therefore, the force was exerted over a distance of 17.28 meters.
To find the distance over which the force was exerted, we can use the concept of work.
Work(W) = Force(F) x Distance(d) x cos(θ)
Where:
W = Work done
F = Force applied
d = Distance over which the force is applied
θ = Angle between the direction of force and the direction of motion
In this case, the angle between the force and the motion is not given. Assuming that the force is applied in the same direction as the motion of the skier, the angle would be 0°, and the cosine of 0° is 1.
So, the formula becomes:
Work(W) = Force(F) x Distance(d)
We know the force applied (F) is 417N. To find the distance (d), we can rearrange the formula:
Distance(d) = Work(W) / Force(F)
The work done can be calculated using the equation:
Work(W) = Change in Kinetic Energy(ΔKE)
The change in kinetic energy of the skier can be calculated using the equation:
ΔKE = (1/2) x m x (v^2 - u^2)
Where:
m = mass of the skier
v = final velocity of the skier
u = initial velocity of the skier (which is 0 as the skier is at rest initially)
Plugging in the values:
m = 64kg
v = 15m/s
u = 0m/s
ΔKE = (1/2) x 64kg x (15m/s)^2
Now, we can calculate the work done using the change in kinetic energy:
W = ΔKE = (1/2) x 64kg x (15m/s)^2
Finally, we can substitute the value of work done and force applied into the distance formula to find the distance over which the force was exerted:
Distance(d) = Work(W) / Force(F)
Distance(d) = [(1/2) x 64kg x (15m/s)^2] / 417N
Calculating this expression will give us the distance over which the force was exerted.