Example 7: How High Does it Go?
A football game customarily begins with a coin toss to determine who kicks off. The referee tosses the coin up with an initial speed of \( 5.00 \mathrm{~m} / \mathrm{s} \). In the absence of air resistance, how high does the coin go above its point of release?
\begin{tabular}{|c|c|c|c|c|}
\hline \multicolumn{5}{|c|}{ Coin Data } \\
\hline \( \boldsymbol{y} \) & \( \boldsymbol{a} \) & \( \boldsymbol{v} \) & \( \boldsymbol{v}_{\boldsymbol{0}} \) & \( \boldsymbol{t} \) \\
\hline\( ? \) & \( -9.8 \mathrm{~m} / \mathrm{s}^{2} \) & \( 0 \mathrm{~m} / \mathrm{s} \) & \( +5.00 \mathrm{~m} / \mathrm{s} \) & \\
\hline
\end{tabular}
Kinematics Practice Problems - Vertical Motion
Problem 1 - Dropping a Tool from a Crane
A construction worker accidentally drops a wrench from a crane 45.0 meters above the ground. Assuming there is no air resistance, the wrench falls freely under gravity. How long does it take for the wrench to reach the ground?
Problem 2 - Basketball Shot to a Hoop
A basketball player jumps and releases the ball from a height of 2.00 meters above the floor, aiming for the hoop 3.05 meters above the floor. The ball reaches the hoop 0.650 seconds after being released, following a straight vertical path. With what vertical velocity was the ball released?
Problem 3 - A Firework Launched Upward
A firework is launched vertically from the ground with an initial velocity of \( 28.0 \mathrm{~m} / \mathrm{s} \). It travels upward until it momentarily stops at the peak of its path. What maximum height does the firework reach above the ground?
Problem 4-Vertical Toss to a Window
A person standing on the ground throws a small package straight upward with an initial velocity of \( 16.0 \mathrm{~m} / \mathrm{s} \). The package is caught by someone at a window 1.50 seconds later. What is the vertical displacement of the package when it is caught7