# Projectile Motion (Initial Velocity)

by Milkster18
Tags: initial, physics, projectile, velocity
 P: 22 Hi, im trying to find the initial velocity of this question: Using a video camera, it is observed that when a ball is kicked from A, it just clears the top of a wall at B as it reaches its maximum height. Knowing the distance from A to the wall is 20m and the wall is 4m high, determine the initial velocity at which the ball was kicked. Neglect size of the ball ( Ans Ua = 23.9m/s). So im thinking to find the angle you have to use trig : so 20^2 + 4^2 = square root of 416 = 20.4m (hypotenuse) using Sin, 4/ 20.4 = Invert Sin 0.196 = 11.3 degrees angle the ball is projected. Now i have then angle what else do i need to find in order to find the initial velocity at which the ball was kicked? Thanks for any help
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P: 40,874
 Quote by Milkster18 So im thinking to find the angle you have to use trig : so 20^2 + 4^2 = square root of 416 = 20.4m (hypotenuse) using Sin, 4/ 20.4 = Invert Sin 0.196 = 11.3 degrees angle the ball is projected.
That angle is not the angle of the ball's initial velocity. The ball travels a parabolic trajectory, not a straight line.

Analyze the vertical motion first. Figure out the vertical component of the initial velocity.
 P: 22 Ah ok, i thought about the ball not traveling in a straight line assuming the angle was wrong at some point. Ok so if 'm trying to analyze the vertical component of the initial velocity im going to use equation: Sy = Uyt + 0.5(ay)t^2 Or Vy^2 = Uy^2 - 2g(Sy) The 2nd equation i'm thinking i should use since it has just one unknown (Uy). Vy = 0, Sy = 4m 0 = Uy^2 - 2(-9.81)(4) I dont want to go further until i know what i'm doing so far is correct..
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P: 40,874

## Projectile Motion (Initial Velocity)

 Quote by Milkster18 Ah ok, i thought about the ball not traveling in a straight line assuming the angle was wrong at some point. Ok so if 'm trying to analyze the vertical component of the initial velocity im going to use equation: Sy = Uyt + 0.5(ay)t^2 Or Vy^2 = Uy^2 - 2g(Sy) The 2nd equation i'm thinking i should use since it has just one unknown (Uy). Vy = 0, Sy = 4m 0 = Uy^2 - 2(-9.81)(4) I dont want to go further until i know what i'm doing so far is correct..
Almost perfect. You have an extra minus sign in your last equation. g is just the magnitude of acceleration, so g = 9.81, not -9.81. (The acceleration is -g = -(9.81) = -9.81 m/s^2.)
 P: 22 Ok so Uy^2 = 2(9.81)(4) + 0 Uy^2 = square root 78.48 Uy =8.86 m/s Correct? What shall i do now? Do i find the time? Sy = Uyt + 0.5(9.81)t^ Sy = 4 + (8.86)t - 4.905t^2 Sy = 12.86t / 4.905^2 4 = 12.86 - 4.905 4 = 7.955 t = square root 0.5 = 0.7s t = 0.7 s .. is this correct so far?
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P: 40,874
 Quote by Milkster18 Ok so Uy^2 = 2(9.81)(4) + 0 Uy^2 = square root 78.48 Uy =8.86 m/s Correct?
Yes. Good.

 Do i find the time? Sy = Uyt + 0.5(9.81)t^ Sy = 4 + (8.86)t - 4.905t^2 Sy = 12.86t / 4.905^2
Right approach, but you messed up the equation:
(1) 4 is the final position, not the initial.
(2) a + bt ≠ (a + b)t

Even easier: What's the average vertical speed? Use that to find the time.
 P: 22 Average vertical speed.. Uy / g 8.86 / 9.81 = 0.9 s? (Sorry im getting tired as its nearly 2am)
 P: 22 speed is calculating in m/s.. sorry im confused
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P: 40,874
 Quote by Milkster18 Average vertical speed.. Uy / g 8.86 / 9.81 = 0.9 s?
No. The vertical speed varies uniformly from its initial value of 8.86 m/s to 0 at the highest point. What do you think the average vertical speed would be?
 P: 22 sice it highest point is Sy = 4m is it 8.86 / 4 = 2.215 m/s average vertical speed? if its not can you provide further help? thanks
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P: 40,874
 Quote by Milkster18 sice it highest point is Sy = 4m is it 8.86 / 4 = 2.215 m/s average vertical speed?
No. You cannot divide a speed by a distance and expect to end up with a speed.

 if its not can you provide further help?
Try this analogy: You start out making zero money and, uniformly, little by little, end up making $100/day. Over that time period, what was your average salary per day? You may want to review some of the basic formulas of kinematics: Basic Equations of 1-D Kinematics Kinematic Equations and Problem-Solving And here's some good stuff about projectile motion: Projectile Motion  P: 22 u+v / 2 = the average? So v = 0 8.86 / 2 = 4.43 m/s Mentor P: 40,874  Quote by Milkster18 u+v / 2 = the average? So v = 0 8.86 / 2 = 4.43 m/s Good! So now that you have the average vertical speed and the vertical distance, figure out the time.  P: 22 with the analogy: Say you made 0$ to 100$over 7 days .. average income per day is 100 / 7 = 14.3$ per day
 P: 22 Sy = (4.43)t - (4.91)t^2 4 = (4.43)t - (4.91) 4 = -0.48? 4 / 0.48 = square root 8.33 t = 2.887 s ?
 P: 22 Question: Why does the AVERAGE Initial vertical velocity have to be used instead of just the initial vertical velocity so i can understand why?
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P: 40,874
 Quote by Milkster18 with the analogy: Say you made 0$to 100$ over 7 days .. average income per day is 100 / 7 = 14.3\$ per day
No. Your income increases from 0/day to 100/day. Like this:
0/day; 1/day, 2/day, 3/day...... 100/day. Average (assuming uniform increase--just like uniform acceleration) is (0 + 100)/2 = 50/day. Half the time you made less, half the time you made more.

(But don't worry about that analogy if it doesn't help.)
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P: 40,874
 Quote by Milkster18 Sy = (4.43)t - (4.91)t^2 4 = (4.43)t - (4.91) 4 = -0.48? 4 / 0.48 = square root 8.33 t = 2.887 s ?
No, using that method you would use the initial velocity, not the average velocity. You'll end up with a quadratic to solve.

 Quote by Milkster18 Question: Why does the AVERAGE Initial vertical velocity have to be used instead of just the initial vertical velocity so i can understand why?
Again, using that method you would use the initial velocity.

I wanted to show you an easier way to get the time, using Distance = ave speed X time. No quadratics to solve. (Do it both ways and compare the answers.)

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