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A ball is thrown upward at a speed $v_{0}$ at an angle of $52^{\circ}$ above the horizontal. It reaches a maximum height of 7.5 m. How high would this ball go if it were thrown straight upward at speed v0?

$y_{\max }^{\prime}=12.08 \mathrm{m}$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

Rutgers, The State University of New Jersey

University of Washington

Simon Fraser University

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

10:12

A vector is a mathematical entity that has a magnitude (or length) and direction. The vector is represented by a line segment with a definite beginning, direction, and magnitude. Vectors are added by adding their respective components, and multiplied by a scalar (or a number) to scale the vector.

02:39

A ball is thrown upward at…

01:25

02:28

02:42

A ball is thrown horizonta…

0:00

A ball is thrown upwards f…

07:14

A ball is shot from the gr…

05:15

02:48

03:20

(a) When a projectile is t…

08:55

A ball is thrown from the …

03:41

A ball is thrown upward wi…

so the questions It's that a projectile shot at a speed V, not an angle with 52 degrees and at its maximum height it reaches 7.5 meters. And we're trying to find how high the project I would go if we shot it straight up with the same speed V. Not so to do this we first came break up RV not, uh velocity vector into components of visa backs. NV said Why? And to do this, we can say that the co sign of 52 degrees is the same thing as adjacent over high Panis. So visa backs over the not which means Visa. Becks is equal to V not co sign of 52 degrees. And the same thing goes for Visa. Why? But instead of co sign it will be assigned. So maybe he not sign of 52 degrees. So now that we have this, we can use our kingdom attics equations to solve for what V not is equal to, um in this case, we're going to use the equation which states that the final velocity squared is equal to the initial velocity squared, plus two times the acceleration times the change in displacement. So we're gonna focus on the vertical component of the velocity for this case. So we know that our final velocity at this maximum height here in the vertical direction is going to be zero. So this will be zero is equal to the initial velocity, which is be not sign 52 degrees. This will be squared plus two times the acceleration which will be due to evidence. So be negative 9.8 times the displacement, which uh is 7.5 meters. So now that we have this, we can solve for what V not is equal to. So if we subject two times negative 9.8 times 7.5 on both sides, we get this and then we can take the square root on both sides. So we'll get square root of two times 9.8 time 7.5 and these minus signs appear. Both cancel out, become positive, be not sign 52 degrees, and then we can divide by sign 52 degrees on both sides. So we'll find that V not will be equal to two times 9.8 times 7.5 all under the square root and then divided by sign of 52 degrees, which is just the same thing as 15 point 386 meters per second. So now that we know what V not is equal to, we can solve for the situation where V not is pointing straight up. So here's not again. And if we do this, we can just use the same exact creation that we did up here. So we know that the final velocity at its maximum height is going to be zero. So this term will cancel out. We know that the initial velocity is just 15 0.3 86 This is all squared. Once again, we know that the acceleration is gonna be negative 9.8. And we know that the, um and we're trying to find what the Delta X is or the change in displacement. So when we work this out so we're gonna subject 15.386 squared on both sides, and then we can divide by two times negative nine playing eight on both sides. And once we do this, we get with Delta X is equal to, And when we simplify this, we find that it's equal to 12.8 meters, and that's the answer

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