Final answer:
To determine the velocity of a projectile at time t after being launched vertically with an initial velocity of 112 ft/s, the kinematic equation v = v0 + at can be used, considering gravity's acceleration of -32.2 ft/s2. This allows the calculation of the projectile's velocity at any given time t during its flight.
Step-by-step explanation:
Finding the Velocity at Time t for a Vertically Launched Projectile
To find the velocity of a projectile at a given time t after being launched vertically upward with an initial velocity, we need to consider the acceleration due to gravity, which is constantly acting on the projectile in the opposite direction of its initial motion. We can use the following kinematic equation which links the final velocity v at time t, the initial velocity v0, the acceleration a, and the time t:
v = v0 + at
For this scenario, the initial velocity v0 is given as 112 ft/s upwards, the acceleration due to gravity a is -32.2 ft/s2 (negative because it acts downward), and we want to find the velocity at an arbitrary time t.
We can rearrange the equation to solve for v as follows:
v = 112 ft/s - (32.2 ft/s2 × t)
This equation will give us the velocity of the projectile at any time t during its flight, with the sign indicating the direction (positive for upwards, negative for downwards). As the projectile rises, gravity slows it down until its velocity reaches zero at its peak, after which the projectile will start to fall back to the ground, speeding up in the negative direction due to gravity.