# Physics

What is the velocity at the midway point of a ball able to reach a height y when thrown with an initial velocity
v0?
(Assume the ball is thrown upward and that up is the positive direction. Use the following as necessary: y and g. )

Someone posted this question before and was given the answer

v= sqrt (v_o)^2 + 9.8y

1. 👍
2. 👎
3. 👁
1. Maybe it is a reading of the question. If the max height is y, midpoint is y/2

If that is so, then the 9.8 should be -9.8, and the equation is dead on correct.

1. 👍
2. 👎
👤
bobpursley
2. The motion to the highest point (height “H”)
v = vₒ - g•t,
v=0, t = vₒ/g.
H = vₒ•t - g•t²/2 = vₒ• vₒ/g –(g/2) •(vₒ/g)² = vₒ²/2•g.
Velocity at the midpoint (height “h“)
v =vₒ - g•t1,
t1 =(vₒ- v)/g.
h = vₒ•t1 - g•t1²/2 =
=vₒ•(vₒ- v)/g - g•(vₒ- v)²/2•g² =
= [2•vₒ•(vₒ- v) -(vₒ- v)²]/ 2•g =
={2vₒ² - 2vₒ•v - vₒ² +2 vₒ•v - v²}/2•g =
= (vₒ² - v²)/2•g.
h=H/2 = vₒ²/2•2•g.
(vₒ² - v²)/2•g = vₒ²/2•2•g.
vₒ² = 2•v²,
v =vₒ/√2 = vₒ/1.41 =0.707•vₒ

1. 👍
2. 👎
3. this came from a test bank so the second answer listed is correct but wasn't an option (you need the negative sign on g), so you had to do what the third person did so that h isn't in the answer. But, h was given in the original question so it should be allowed in the answer and I like the 2nd answer better.

1. 👍
2. 👎
4. Yes

1. 👍
2. 👎

## Similar Questions

1. ### Physics

A tennis ball is thrown vertically upward with an initial velocity of +8.0 m/s. a. what will the ball's speed be when it returns to its starting point? b. how long will the ball take to reach its starting point?

2. ### Physics

A tennis player hits a ball at ground level, giving it an initial velocity of 24 m/s at 57 degrees above the horizontal. (a) what are the horizontal and verticla components of the ball;s initial velocity? (b) how high above the

3. ### pre-calc

Physics: a ball is thrown vertically upward with an initial velocity of 80 feet per second. the distance (in feet) of the ball from the ground after t seconds if s=80t-16tt^2 a) draw the illustration b) for what time interval is

4. ### Physics

From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 8.00 m/s and angle of 20.0 degrees below the horizontal. It strikes the ground 3.00 s later. (a) If the base of the

1. ### Physics

A ball is thrown vertically upward with a speed of 25.0 m/s from a height of 2.0 m. How high does the ball rise? How long does it take to reach its highest point? How long does the ball take to hit the ground after it reaches its

2. ### physics

A ball is dropped from a height of 1.5m. how long will it take the ball to reach the ground and what velocity will it reach?

A ball is thrown vertically upwards From the top of a building of height 29.4 m and with an initial velocity 24.5 m/sec. If the height H of the ball from the ground level is given by H = 29.4 + 24.5t - 4.9t², then find the time

4. ### Algebra 1

A baseball is thrown into the air with an upward velocity of 30 ft/s. Its height h, in feet, after t seconds is given by the function h=-16t^2+6. How long will it take the ball to reach its maximum height? What is the ball's

1. ### Physics

If the soccer player kicks the ball with an initial velocity of 20 m/s at an angle of 45 degrees relative to the ground then what is the time it takes for the ball to reach the maximum height, what is the time of flight, what is

2. ### physics

A ball is thrown upward with an initial velocity of 13 m/s. At what time does the ball reach the high point in its flight? (Use the approximate value of g = 10 m/s2, and remember that the velocity is equal to zero at the high

3. ### Physics

You toss a tennis ball straight upward. At the moment it leaves your hand it is at a height of 1.5 m above the ground, and it is moving at a speed of 7.8 m/s. (a) How much time does it take for the tennis ball to reach its maximum

4. ### physics

A tennis ball is thrown vertically upward with an initial velocity of +7.5 m/s. What will the ball’s velocity be when it returns to its starting point? The acceleration of gravity is 9.81 m/s 2 . Answer in units of m/s How long