A ball is thrown horizontally from a height of 100 m. It covered a horizontal distance of 3,350
m when it touches the ground.
a. What is its horizontal velocity?
b. How many seconds after it was fired will it touch the ground?
c. What was its vertical velocity when it hits the ground?
a) 100 = 1/2(9.8)t^2
v = x/t
b) See a)
c)v = 9.8t
To solve these questions, we need to use the equations of motion for both horizontal and vertical motion.
a. To find the horizontal velocity, we can use the formula:
Horizontal distance = Horizontal velocity × Time
Rearranging the formula gives:
Horizontal velocity = Horizontal distance / Time
Plugging in the given values, we have:
Horizontal distance = 3,350 m
Time = ?
To find the time, we need to know the vertical motion of the ball. Let's move on to question b to find the answer.
b. To find the time it takes for the ball to touch the ground, we can use the vertical motion equation:
Vertical distance = Initial vertical velocity × Time + (1/2) × Acceleration due to gravity × Time^2
Since the ball is thrown horizontally and there is no vertical initial velocity, the first term becomes zero:
Vertical distance = (1/2) × acceleration due to gravity × Time^2
Plugging in the values, we have:
Vertical distance = 100 m
Acceleration due to gravity = 9.8 m/s^2
Rearranging the formula gives:
Time^2 = (2 × Vertical distance) / acceleration due to gravity
Time = sqrt((2 × Vertical distance) / acceleration due to gravity)
Plugging in the given values, we find:
Time = sqrt((2 × 100) / 9.8) = sqrt(20.41) = 4.52 seconds
Now that we know the time it takes for the ball to touch the ground, we can go back to question a to find the horizontal velocity.
Horizontal velocity = Horizontal distance / Time
Horizontal velocity = 3,350 m / 4.52 s = 741.59 m/s
c. To find the vertical velocity when the ball hits the ground, we can use the equation:
Final vertical velocity = Initial vertical velocity + (Acceleration due to gravity × Time)
Since the ball is thrown horizontally, the initial vertical velocity is zero:
Final vertical velocity = Acceleration due to gravity × Time
Plugging in the values, we have:
Acceleration due to gravity = 9.8 m/s^2
Time = 4.52 s
Final vertical velocity = 9.8 m/s^2 × 4.52 s = 44.30 m/s
Therefore, the answers are:
a. The horizontal velocity of the ball is 741.59 m/s.
b. The ball will touch the ground approximately 4.52 seconds after it was fired.
c. The vertical velocity of the ball when it hits the ground is 44.30 m/s.