A 1.2kg lead ball is launched off a cliff top at 16m/s at an angle of 20 degrees above the horizontal. The height of the horizontal is 15m. Determine the net force acting on the lead ball that caused the ball to drop 4.0m from point P.
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To determine the net force acting on the lead ball, we first need to break down the motion into horizontal and vertical components.
1. Calculate the horizontal component of the initial velocity:
- The horizontal component of the velocity can be found using the formula:
vx = v * cos(theta)
Where:
- vx is the horizontal component of the velocity
- v is the initial velocity of the ball (16m/s)
- theta is the angle between the initial velocity and the horizontal (20 degrees)
Plugging in the values, we have:
vx = 16 * cos(20)
2. Calculate the vertical component of the initial velocity:
- The vertical component of the velocity can be found using the formula:
vy = v * sin(theta)
Where:
- vy is the vertical component of the velocity
- v is the initial velocity of the ball (16m/s)
- theta is the angle between the initial velocity and the horizontal (20 degrees)
Plugging in the values, we have:
vy = 16 * sin(20)
3. Calculate the time of flight:
- The time of flight can be found using the formula:
t = 2 * vy / g
Where:
- t is the time of flight
- vy is the vertical component of the velocity (calculated in step 2)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Plugging in the values, we have:
t = 2 * vy / g
4. Calculate the acceleration in the vertical direction:
- The acceleration in the vertical direction can be found using the formula:
a = -2 * (h - y) / t^2
Where:
- a is the acceleration
- h is the height of the cliff (15m)
- y is the vertical displacement of the ball (4.0m)
- t is the time of flight (calculated in step 3)
Plugging in the values, we have:
a = -2 * (15 - 4) / t^2
5. Calculate the net force acting on the lead ball:
- The net force can be found using the formula:
F = m * a
Where:
- F is the net force
- m is the mass of the lead ball (1.2kg)
- a is the acceleration (calculated in step 4)
Plugging in the values, we have:
F = 1.2 * a
By following these steps and plugging in the appropriate values, you will be able to determine the net force acting on the lead ball that caused it to drop 4.0m from point P.