Question

A plane is flying east when it drops some supplies to a designated target below. The supplies land after falling for 10 seconds. How high above the ground was the airplane when the supplies were dropped? (Hint: d = 1/2gt2; g = -9.8 m/s2)

Question 3 options:

120 meters


490 meters


980 meters


49 meters

Question 4 (10 points)
As the supplies fell, they traveled 650 meters horizontally. How fast were the supplies and the airplane moving forward? Remember that it took 10 seconds for them to reach the ground. (Hint: v = d/t)

Question 4 options:

65 m/s


6500 m/s


0.154 m/s


660 m/s

Question 5 (10 points)
A projectile has a vertical component and a horizontal component.

Question 5 options:
True
False
Question 6 (10 points)
The shape of a projectile's trajectory is an ellipse.

Question 6 options:
True
False
Question 7 (10 points)
Which of the following is not true about a vertical component?

Question 7 options:

The vertical component of a projectile changes due to gravity.


The vertical component acts the same as an object in free fall.


The vertical component always equals the horizontal component.

Question 8 (10 points)
During the course of trajectory, the horizontal component of the velocity is

Question 8 options:

constant


increasing


decreasing


negative

Answer 1

3)  490 meters

The vertical motion of the supplies is an accelerated motion with constant acceleration g=-9.8 m/s^2, so its vertical position is given by

$y(t)=h+\frac{1}{2}gt^2$

where h is the initial height of the airplane, and t is the time taken. Substituting y(t)=0 and t=10 s (when the supplies reach the ground), we find the height h:

$0=h+\frac{1}{2}gt^2\\h=-\frac{1}{2}gt^2=-\frac{1}{2}(-9.8 m/s^2)(10 s)^2=490 m$

4) 65 m/s

The horizontal motion of the supplies is a uniform motion with constant speed v, which is given by the ratio between the distance travelled and the time taken:

$v=\frac{d}{t}=\frac{650 m}{10 s}=65 m/s$

5) True

A projectile has two independent motions:

- A horizontal motion, which is a uniform motion with constant horizontal speed

- A vertical motion, which is an accelerated motion with constant acceleration equal to the gravitational acceleration (g=9.8 m/s^2) directed downward

6) False

The trajectory of a projectile is a parabola, which is the composition of the two independent motions along the horizontal and vertical directions.

7) The vertical component always equals the horizontal component.

This statement is false. In fact, the horizontal component of the velocity of a projectile is:

$v_x = v_0 cos \theta$

while the vertical component of the initial velocity of the projectile is

$v_y = v_0 sin \theta$

So, we see that they are not always equal.

8) constant

In fact, there are no forces acting along the horizontal direction of the projectile's motion: therefore, the horizontal acceleration is zero, and so the horizontal velocity is constant.