At the instant a race began, a 74.0 kg sprinter exerted a force of 850 N on the starting block at a 23.0 degree angle with respect to the ground. what was the horizontal acceleration of the sprinter?
To find the horizontal acceleration of the sprinter, we need to determine the horizontal component of the force applied on the starting block.
The horizontal component of the force can be found using the formula:
Force_horizontal = Force * cos(angle)
where Force is the magnitude of the force applied (850 N) and angle is the angle with respect to the ground (23.0 degrees).
Plugging in the values, we get:
Force_horizontal = 850 N * cos(23.0°)
Calculating the result, we get:
Force_horizontal ≈ 850 N * cos(23.0°)
Force_horizontal ≈ 850 N * 0.9205
Force_horizontal ≈ 782.43 N
The horizontal acceleration of the sprinter is equal to the force divided by the mass of the sprinter:
Acceleration_horizontal = Force_horizontal / mass
Plugging in the values, we get:
Acceleration_horizontal = 782.43 N / 74.0 kg
Calculating the result, we get:
Acceleration_horizontal ≈ 10.57 m/s²
Therefore, the horizontal acceleration of the sprinter is approximately 10.57 m/s².
To find the horizontal acceleration of the sprinter, we need to resolve the force vector into its horizontal and vertical components. The horizontal component of the force will determine the accelerated motion of the sprinter in the horizontal direction.
To resolve the force into its components, we can use trigonometry. The horizontal component of the force can be found using the formula:
F_horizontal = F * cos(theta)
where F is the magnitude of the force (850 N) and theta is the angle (23.0 degrees).
Plugging in the values:
F_horizontal = 850 N * cos(23.0 degrees)
Now, we can calculate the horizontal component of the force:
F_horizontal ≈ 850 N * 0.9205
F_horizontal ≈ 782.425 N
Since force is related to acceleration by Newton's second law (F = m * a), we can find the horizontal acceleration (a_horizontal) by rearranging the equation:
a_horizontal = F_horizontal / m,
where m is the mass of the sprinter (74.0 kg).
Plugging in the values:
a_horizontal = 782.425 N / 74.0 kg
Now we can calculate the horizontal acceleration:
a_horizontal ≈ 10.57 m/s^2
Therefore, the horizontal acceleration of the sprinter is approximately 10.57 m/s^2.