Question

A shotputter can exert 80 lb of force on a 16-lb (i.e.,0.5-slug) shot. If he directs this force at 50o to the horizontal, what is the magnitude of its horizontal acceleration?

Answer 1

The magnitude of the horizontal acceleration of the shot is approximately 1629.85 ft/s^2.

Step-by-step explanation:

To find the magnitude of the horizontal acceleration of the shot, we can use Newton's second law of motion, which states that force is equal to mass times acceleration. In this case, the shot has a mass of 16 lb or 0.5 slugs. The force exerted by the shot putter is 80 lb. The horizontal component of the force can be found using trigonometry:

Force horizontal = Force total * cos(theta)

where theta is the angle of the force with respect to the horizontal. In this case, theta is 50 degrees. So,

Force horizontal = 80 lb * cos(50 degrees)

Using a calculator, we can find that the horizontal component of the force is approximately 51.27 lb. We can then use Newton's second law to find the acceleration:

Acceleration horizontal = Force horizontal / mass

Substituting the values, we get:

Acceleration horizontal = 51.27 lb / 0.5 slugs

Converting lb to slugs, we get:

Acceleration horizontal = 51.27 slugs * ft/s^2 (1 slug = 32.174 ft/s^2)

So the magnitude of the horizontal acceleration is approximately 1629.85 ft/s^2.