1) Throw a small ball (best a golf ball) straight upward as...

1) Throw a small ball (best a golf ball) straight upward as hard as you can. Your friend can measure the time of flight of the ball using a stop watch. Find the initial speed of your throw and the approximate maximum height of the ball solely with the use of the measured time. Please write here the equations you are using: Time of Flight ~ 2v/g hmax ~ v^2/2g Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 t 2.87 2.54 2.94 3.19 2.53 Vo 14.1 hmax 10.1

Transcript

00:01 Our system here is a golf ball that is thrown vertically upward and then the time it takes to be airborne is measured as given in the five trials here in the data sheet.

00:15 We are to determine the corresponding initial speed and the maximum height achieved by the ball in each trial.

00:25 So since the ball here is undergoing a free fall where an air existence, air resistance is neglected and the acceleration along the y is due to up to gravity then among the free fall equations the easy as to use in determining the initial speed would be this equation which says that the velocity of the particle along the y final velocity is equivalent to the initial velocity along the y minus acceleration due to gravity times time since the golf ball here has no x component in its initial velocity then if you're able to solve for the y component of the initial velocity then that will already be the initial velocity that is required to to be determined okay so let's simplify this and take note that the y component we now consider it as the initial velocity, the magnitude would be the initial speed.

01:37 At the highest point, so at the highest point here, the velocity of the highest point is zero.

01:50 So our main equation now becomes, it's supposed to this negative gt on the other side so that it becomes positive.

01:56 Then this is now our equation for the initial speed.

02:03 So let's call this equation 1.

02:05 And the other one for h maximum, we will use this equation.

02:10 Dy squared is equal to d -o -y -squared minus 2 times acceleration due to gravity.

02:18 And the change in position we'll call it now as h -max, because we'll consider that the initial position of the golf ball at the thrower's hand is zero.

02:33 So we still use the point in the motion where it reaches the highest point.

02:42 So again, it has no vy, so this is zero.

02:45 Then we transpose this term, the other side, so that it becomes positive to g.

02:56 H maximum and then v -o -y will just call it a space of o squared.

03:03 Isolating h -max in the left -hand side, we have the square of the initial speed divided by two times acceleration due to gravity...

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