Question

consider a projectile fired vertically in a constant gravitational field. for the same initial velocities, find the times required for the projectile to reach its maximum height (a) with no resisting force and (b) for a resisting force proportional to the instantaneous velocity of the projectile. (c) show that the result in (a) can be recovered from the result in (b).

Answer 1

The time required for a projectile to reach its maximum height can be determined using the equations t = v_y / g for no resisting force and t = (2v_y) / g for a resisting force proportional to the instantaneous velocity. The result in (a) can be recovered from the result in (b) by setting the resisting force to zero.

Step-by-step explanation:

The time required for a projectile to reach its maximum height with no resisting force is determined solely by its vertical motion. For a projectile fired vertically in a constant gravitational field, the time to reach maximum height can be found using the equation:

t = vy / g, where t is the time, vy is the initial vertical velocity, and g is the acceleration due to gravity.

For a projectile with a resisting force proportional to the instantaneous velocity, the time to reach maximum height can be found using more complex equations, such as the time of flight formula:

t = (2vy) / g.

The result in (a), where no resisting force is present, can be recovered from the result in (b) by setting the resisting force to zero. In that case, the equation for the time to reach maximum height becomes the same as in (a), t = vy / g.