The boy on the tower (20 m) throws a ball a distance of 60 m. At what speed, in m/s, is the ball thrown?
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Thanks!!
Well, since the ball was thrown a distance of 60 m and the tower is 20 m high, I'd say this boy has quite the arm! It's like he's trying out for the Olympic baseball team or something. But let's not get carried away with dreams of fame and fortune. We need to figure out the speed of the ball.
To do that, we can use the equation for speed: speed = distance/time. In this case, the distance is 60 m. But we don't know the time it took for the ball to travel that distance.
If we assume that the ball was thrown horizontally, we can use the time it takes for the ball to hit the ground after being thrown from the top of the tower. So, how about we calculate that?
The time it takes for an object to fall from a certain height can be determined using the equation: time = sqrt(2 * height / g), where g is the acceleration due to gravity (approximately 9.8 m/s^2).
In this case, the height is 20 m, so let's plug it into the equation: time = sqrt(2 * 20 / 9.8).
Calculating that, we find that it takes approximately 2 seconds for the ball to hit the ground.
Now, we have the time, so we can calculate the speed. Speed = distance/time. Plugging in the values, we get: speed = 60/2.
Doing the math, the speed of the ball is approximately 30 m/s.
So, the boy threw the ball with a speed of 30 m/s. Keep practicing, kiddo! Maybe one day you'll be the star pitcher for a professional team.
To find the speed at which the ball is thrown, we need to divide the distance it travels by the time it takes to travel that distance.
Given that the ball is thrown a distance of 60 m, we need to determine the time it takes for the ball to travel this distance.
To calculate the time it takes for the ball to fall from the tower and reach the ground, we can use the following formula:
time = √(2 * height / g)
Where:
- g is the acceleration due to gravity, which is approximately 9.8 m/s^2, and
- height is the initial vertical distance, which is 20 m.
Substituting these values, we get:
time = √(2 * 20 / 9.8)
= √(40 / 9.8)
≈ √4.0816
≈ 2.02 s
Now, since the ball was thrown horizontally, it traveled a distance of 60 m during this time.
Therefore, the speed at which the ball is thrown is:
speed = distance / time
= 60 m / 2.02 s
≈ 29.70 m/s
Therefore, the ball is thrown at a speed of approximately 29.70 m/s.
To calculate the speed at which the ball is thrown, we need to use the equation:
speed = distance / time
In this case, the distance the boy throws the ball is given as 60 m. However, we don't have the time taken for the ball to cover this distance directly.
To find the time taken, we need to use the equation for the vertical motion of the ball:
distance = initial velocity * time + 0.5 * acceleration * time^2
Since the ball is thrown vertically upward and eventually comes to rest at the top of its trajectory, we know that the final velocity is zero. The acceleration due to gravity is approximately -9.8 m/s^2. The distance traveled vertically is 20 m.
Using these values, we can rearrange the above equation to find the time taken to reach the maximum height (when the ball is thrown vertically):
0 = initial velocity * time + 0.5 * acceleration * time^2
Simplifying this equation, we get:
0 = initial velocity * time - 4.9 * time^2
Now, solving for time using the quadratic formula, we find:
t = [ -initial velocity ± sqrt(initial velocity^2 - 4*(-4.9)*0) ] / (2*(-4.9))
Since we know the initial velocity is what we're trying to find, we can choose the positive root of the quadratic equation. This is because throwing the ball vertically upward will result in a positive initial velocity.
Simplifying further, we have:
t = [ -initial velocity ± sqrt(initial velocity^2) ] / (2*(-4.9))
t = [ -initial velocity ± initial velocity ] / (-9.8)
t = initial velocity / 9.8
Now, we can substitute this value for time into the equation for speed:
speed = distance / time
speed = 60 / (initial velocity / 9.8)
speed = 588 / initial velocity
From here, we can re-arrange the equation to solve for the initial velocity:
initial velocity = 588 / speed
Therefore, to find the speed at which the ball is thrown, divide 588 by the given speed in m/s.
I have to assume the ball was thrown horizontally.
Find the time for a ball 20 m high to hit the ground
h=1/2 g t^2
then, 60m=velocity*time solve for velocity