You can use any coordinate system you like to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity v → at an angle θ with respect to the horizontal. Let the building be 50.0 m tall, the initial horizontal velocity be 9.00 m/s, and the initial vertical velocity be 12.0 m/s. Choose your coordinates such that the positive y -axis is upward, the x -axis is to the right, and the origin is at the point where the ball is released, (a) With these choices, find the ball’s maximum height above the ground and the time it takes to reach the maximum height. (b) Repeat your calculations choosing the origin at the base of the building.
You can use any coordinate system you like to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity v → at an angle θ with respect to the horizontal. Let the building be 50.0 m tall, the initial horizontal velocity be 9.00 m/s, and the initial vertical velocity be 12.0 m/s. Choose your coordinates such that the positive y -axis is upward, the x -axis is to the right, and the origin is at the point where the ball is released, (a) With these choices, find the ball’s maximum height above the ground and the time it takes to reach the maximum height. (b) Repeat your calculations choosing the origin at the base of the building.
Solution Summary: The following diagram shows the projection of ball from the top of the building.
You can use any coordinate system you like to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity
v
→
at an angle θ with respect to the horizontal. Let the building be 50.0 m tall, the initial horizontal velocity be 9.00 m/s, and the initial vertical velocity be 12.0 m/s. Choose your coordinates such that the positive y-axis is upward, the x-axis is to the right, and the origin is at the point where the ball is released, (a) With these choices, find the ball’s maximum height above the ground and the time it takes to reach the maximum height. (b) Repeat your calculations choosing the origin at the base of the building.
From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 8.60 m/s and angle of 18.0° below the horizontal. It strikes the ground 5.00 s later.
(a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0.)
xi
=
0
yi
=
γ0
(b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity.
vi,x
=
m/s
vi,y
=
m/s
(c) Find the equations for the x- and y- components of the position as functions of time. (Use the following as necessary: y0 and t. Let the variable t be measured in seconds.)
x
=
m
y
=
m
(d) How far horizontally from the base of the building does the ball strike the ground? m(e) Find the height from which the ball was thrown. m(f) How long does it take the ball to reach a point 10.0…
ANSWER THE LETTER D, E, AND F ONLY
From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 6.50 m/s and angle of 25.0° below the horizontal. It strikes the ground 4.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. (c) Find the equations for the x- and y-components of the position as functions of time. (d) How far horizontally from the base of the building does the ball strike the ground? (e) Find the height from which the ball was thrown. (f) How long does it take the ball to reach a point 12.0 m below the level of launching?
A stone is catapulted at time t = 0, with an initial velocity of magnitude 20.5 m/s and at an angle of 40.2° above the horizontal. What are
the magnitudes of the (a) horizontal and (b) vertical components of its displacement from the catapult site at t = 1.13 s? Repeat for the
(c) horizontal and (d) vertical components at t = 1.77 s, and for the (e) horizontal and (f) vertical components at t = 5.47 s. Assume that
the catapult is positioned on a plain horizontal ground.
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