Question

question 5 of 25
a boy throws a ball up into the air with a speed of 8.2 m/s. the ball has a
mass of 0.3 kg. how much gravitational potential energy will the ball have at
the top of its flight? (assume there is no air resistance.)
a. 15.2 j
b. 19.3 j
c. 10.1 j
d. 8.7 j

Explanation:

Step1: Apply the conservation of mechanical energy

At the bottom (when thrown), the ball has kinetic energy \(K = \frac{1}{2}mv^{2}\), and at the top of its flight, its kinetic energy is \(K = 0\) (since vertical - velocity \(v_y=0\) at the top of the flight for vertical motion) and its potential energy \(U = mgh\). By the conservation of mechanical energy (since there is no air - resistance, \(E_{initial}=E_{final}\)), the initial kinetic energy is converted into potential energy. The formula for kinetic energy is \(K=\frac{1}{2}mv^{2}\), where \(m = 0.3\space kg\) and \(v = 8.2\space m/s\).

Step2: Calculate the kinetic energy

Substitute the values into the kinetic - energy formula \(K=\frac{1}{2}mv^{2}\).

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Answer:

C. 10.1 J