To determine the magnitude of the horizontal force acting on the sprinter, we can break down the solution into two parts: finding the sprinter's acceleration and then using Newton's second law to calculate the force.

Step 1: Calculate Acceleration

Since the sprinter starts from rest, we can use the kinematic equation: $d = \frac{1}{2} a t^2$ where:

• $d = 45 \, \text{m}$ (distance traveled),
• $t = 7.0 \, \text{s}$ (time taken),
• $a$ is the acceleration.

Rearranging for $a$: $a = \frac{2d}{t^2}$ Substitute the values: $a = \frac{2 \times 45 \, \text{m}}{(7.0 \, \text{s})^2} = \frac{90}{49} \approx 1.84 \, \text{m/s}^2$

Step 2: Calculate Force

Using Newton's second law, $F = ma$, where:

• $m = 65 \, \text{kg}$ (mass of the sprinter),
• $a \approx 1.84 \, \text{m/s}^2$.

Thus: $F = 65 \, \text{kg} \times 1.84 \, \text{m/s}^2 \approx 119.6 \, \text{N}$

Answer

The magnitude of the horizontal force acting on the sprinter is approximately: $\boxed{119.6 \, \text{N}}$

Would you like more details or have any questions?

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1. What if the mass of the sprinter changed to 70 kg?
2. How would the force change if the acceleration were doubled?
3. What if the sprinter covered 50 m instead of 45 m in the same time?
4. How would air resistance affect the actual force needed?
5. How is the force affected by running on a sloped surface?

Tip: Always check if the motion is under constant acceleration when using kinematic equations like $d = \frac{1}{2} a t^2$.