Final answer:
a. The diver will take approximately 1.01 seconds to reach the swimmer. b. The diver's initial speed in the horizontal direction was approximately 3.96 m/s. c. The diver's final velocity as he reached the swimmer was approximately -9.90 m/s.
Step-by-step explanation:
To answer the given questions:
- a. To find the time it takes for the diver to reach the swimmer, we can use the equation:
- Y = Y0 + V0Y*t + 0.5*aY*t^2
- Where:
- Y = Final position (height of the swimmer) = -4 m (negative because we take upward motion as positive)
- Y0 = Initial position (height of the diver) = 5 m
- V0Y = Initial vertical velocity of the diver = 0 m/s (since the diver starts from rest)
- t = Time
- aY = Vertical acceleration = -9.8 m/s^2 (negative because the acceleration is downward)
- Substituting these values into the equation, we have:
- -4 = 5 + 0 + 0.5*(-9.8)*t^2
- 10 = 9.8*t^2
- t^2 = 10/9.8
- t = √(10/9.8) ≈ 1.01 s
- b. To find the initial horizontal speed of the diver, we can use the equation:
- x = x0 + V0X*t
- Where:
- x = Horizontal position of the swimmer = 4 m
- x0 = Initial horizontal position of the diver = 0 m
- V0X = Initial horizontal velocity of the diver = ? (unknown)
- t = 1.01 s (from part a)
- Substituting these values into the equation, we have:
- 4 = 0 + V0X*1.01
- V0X = 4/1.01 ≈ 3.96 m/s
- c. The final velocity of the diver when he reaches the swimmer will depend on the horizontal and vertical components of his velocity. Since there is no horizontal acceleration, the horizontal velocity will remain constant at 3.96 m/s. The vertical velocity can be found using the equation:
- VY = V0Y + aY*t
- Where:
- VY = Final vertical velocity
- V0Y = Initial vertical velocity (0 m/s)
- aY = Vertical acceleration (-9.8 m/s^2)
- t = 1.01 s (from part a)
- Substituting these values into the equation, we have:
- VY = 0 + (-9.8)*1.01
- VY ≈ -9.90 m/s (negative because the velocity is downward)