Final answer:
a. The ball takes 4.6 seconds to hit the water. b. The velocity of the ball when it is 16m below the cliff is 3.5 m/s.
Step-by-step explanation:
To solve this problem, we can break down the initial velocity into its horizontal and vertical components. The horizontal component will remain constant throughout the motion, while the vertical component will be affected by gravity.
a. How long does it take for the ball to hit the water?
To find the time taken, we can use the vertical motion equation which states that the final position (y) is equal to the initial position (y0) plus the initial vertical velocity (v0y) multiplied by time (t), minus half the acceleration due to gravity (g) multiplied by the square of time.
Using the given information:
Initial vertical velocity, v0y = initial speed * sin(angle)
Initial position, y0 = height of the cliff
Final position, y = 0 (at water level)
Acceleration due to gravity, g = 9.8 m/s^2
Substituting the values into the equation and solving for time (t), we get:
t = sqrt(2 * (y - y0) / g)
Now we can substitute the values into the equation:
t = sqrt(2 * (0 - 102) / 9.8) = 4.6 seconds (rounded to one decimal place)
b. What is the velocity when the ball is 16m below the cliff?
We have the initial velocity components and the height below the cliff. To find the final velocity, we can use the vertical motion equation again, substituting the values into the equation:
v = v0y - g * t
Substituting the values into the equation:
v = initial speed * sin(angle) - g * t
v = 85 * sin(26) - 9.8 * 4.6 = 3.5 m/s (rounded to one decimal place)