A 10.67 kg bowling ball has speed 4.35 m/s before hitting the floor. A(n) 66.5 g golf ball flies at much higher speed, so the two balls have exactly same kinetic energy. What is the speed of the golf ball?
Note: neglect rotation of either ball. Answer in units of m/s.
m1= 10.67 kg, v1 = 4.35 m/s, m2 = 0.0665 kg, v2 = ?
m1•v1²/2 = m2•v2²/2,
v2 = v1•sqrt(m1/m2) = 55.1 m/s.
To find the speed of the golf ball, we can use the equation for kinetic energy: KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass, and v is the velocity.
Given that the bowling ball has a mass of 10.67 kg and a speed of 4.35 m/s, we can calculate its kinetic energy. Plugging the values into the equation, we get:
KE_bowling = 1/2 * 10.67 kg * (4.35 m/s)^2
Next, we can set the kinetic energy of the golf ball equal to the kinetic energy of the bowling ball, since both are said to be the same. The golf ball has a mass of 66.5 g, which is equivalent to 0.0665 kg. The velocity we need to find is labeled as v_golf.
Therefore, we have:
KE_bowling = KE_golf
1/2 * 10.67 kg * (4.35 m/s)^2 = 1/2 * 0.0665 kg * v_golf^2
Now we can solve for v_golf by rearranging the equation and then taking the square root of both sides to eliminate the square term:
v_golf = sqrt((10.67 kg * (4.35 m/s)^2) / (0.0665 kg))
Evaluating this expression, we get the speed of the golf ball:
v_golf ≈ 96.13 m/s
Therefore, the speed of the golf ball is approximately 96.13 m/s.