If an object is shot upward with an initial velocity, \( v_{0} \), In feet per second ( \( \mathrm{ft} / \mathrm{s} \) ), the velocity, \( v_{\text {}} \), in \( \mathrm{ft} / \mathrm{s} \) is given by the formula \( v=v_{0}-32 t \), where \( f \) is time in seconds. Find the initial velocity of an object if the velocity after 3 seconds is \( 21 \mathrm{ft} / \mathrm{s} \).

To find the initial velocity \( v_0 \) of the object, we can use the formula \( v = v_0 - 32t \). We know the velocity after 3 seconds (\( t = 3 \)) is \( 21 \mathrm{ft/s} \). Plugging in these values: \[ 21 = v_0 - 32 \cdot 3 \] This simplifies to: \[ 21 = v_0 - 96 \] To find \( v_0 \), add 96 to both sides: \[ v_0 = 21 + 96 = 117 \mathrm{ft/s} \] So, the initial velocity of the object is \( 117 \mathrm{ft/s} \). Initially, when calculating motion, it’s essential to remember that gravity accelerates all objects downward at approximately \( 32 \mathrm{ft/s^2} \) near Earth's surface. This principle helped shape many modern sports and activities, such as skydiving and bungee jumping! If you’re ever unsure while solving similar physics problems, double-check your calculations for any signs or arithmetic errors. Remember, in equations involving time, the time unit must always be consistent, which can save you from unnecessary confusion!