Final answer:
To find the velocity of the golf ball when it returns to its initial starting point, we can use the equations of motion for projectile motion. It takes 4 seconds for the golf ball to reach its highest point, and the total time for it to return to its starting point is 8 seconds. The velocity of the golf ball when it returns to its starting point is -80 m/s.
Step-by-step explanation:
To find the velocity of the golf ball when it returns to its initial starting point, we can use the equations of motion for projectile motion. Since the golf ball is thrown straight up, it will travel upward until it reaches its highest point and then fall back down. The time it takes for the golf ball to reach its highest point is given by the equation:
t = (v - u) / a
Where:
- t is the time
- v is the final velocity (0 m/s at the highest point)
- u is the initial velocity (40 m/s)
- a is the acceleration due to gravity (-10 m/s²)
Substituting the given values into the equation, we have:
t = (0 - 40) / (-10) = 4 seconds
Therefore, it takes 4 seconds for the golf ball to reach its highest point. Since the total time for the golf ball to return to its starting point is twice the time it takes to reach the highest point, the total time is 8 seconds. The velocity of the golf ball when it returns to its starting point is given by the equation:
v = u + at
Substituting the given values into the equation, we have:
v = 40 + (-10)(8) = -80 m/s
Therefore, the velocity of the golf ball when it returns to its initial starting point is -80 m/s.