A stone is thrown from the top of a building upward at an angle of 22.0°
to the horizontal with an initial speed of 20.9 m/s as shown in the figure.
The height of the building is 45.0 m.
(A) How long does it take the stone to reach the ground?
(B) What is the speed of the stone just before it strikes the ground?
A stone is thrown from the top of a building.
Conceptualize Study the figure, in which we have indicated the trajectory and
various parameters of the motion of the stone.
Categorize We categorize this problem as a projectile motion problem. The stone is
modeled as a particle under constant acceleration in the y direction and a
particle under constant velocity in the x direction.
Analyze We have the information xi = yi = 0,
yf = -45.0 m, ay = -g, and vi =
20.9 m/s (the numerical value of
yf is negative because we have chosen the top of the
building as the origin).
(A) How long does it take the stone to reach the ground?
Find the initial x and y components of the stone's velocity:
vxi = vi cos θi
= (20.9 m/s) cos 22.0° = Enter a number.
1 m/s
vyi = vi sin θi =
(20.9 m/s) sin 22.0° = Enter a number.
2 m/s
Express the vertical position of the stone from the vertical component of Equation 4.9:
yf = yi + vyit + ½ayt2
Substitute numerical values:
-45.0 m = (7.829 m/s)t + ½(-9.80 m/s2)t2
Solve the quadratic equation for t:
t = Enter a number.
3 s
(B) What is the speed of the stone just before it strikes the ground?
Use the y component of Equation 4.8 with t = 3.933 s to obtain the y component of the velocity of the stone just before it strikes the ground:
vyf = vyi + ayt
Substitute numerical values:
vyf = 7.829 m/s + (-9.80 m/s2)(3.933 s) = Enter a number.
4 m/s
Use this component with the horizontal component
vxf =
vxi = 19.378 m/s to find the speed of the stone
at t = 3.933 s:
vf = √vxf2 + vyf2 =
√(19.378 m/s)2 + (-30.713 m/s)2
= Enter a number.
5 m/s
Finalize Is it reasonable that the y component of the final velocity
is negative? Is it reasonable that the final speed is larger than the initial
speed of 20.9 m/s?
The following questions present a twist on the scenario above to test your understanding.
Suppose another stone is thrown horizontally from the same building. If it strikes the ground 57 m away, find the following values.
If the stone were thrown harder, and left with 1.5 times the initial speed, you might expect it to go farther, but how exactly does
that happen?
Watch a Video Hint
Note from WebAssign
If a student makes one of several common mistakes on the Master It portion above, they will get feedback specific to the mistake they made. If their answer is incorrect but does not meet one of these specific conditions, they will still get generic numerical feedback as to how far off they are, or if they appear to have made just a sign or order of magnitude error, etc.
Try some of these values for part a to see what feedback you get!
| Incorrect formula | Incorrect answer |
|---|
 | Answers may vary |
 | 29.7 |
 | 883 |
 | 3.41 |
| Correct formula | Correct answer |
|---|
 | 3.03 |