1- A ball is kicked from the ground with a speed of 50 m/s and a direction of 35o above

the horizontal. Calculate:

(i) Its velocity and displacement after 2 seconds

(ii) Its maximum height

(iii) The time it takes to return to the ground

(iv) Its horizontal range

Solution:

��� = � ���� = �� � = �� ��

��� = � ���� = �� � = ��. � ��

(i) �� = ��. � − �. ���� = �. � �/�

|�| = ���� + ��� = √�"�� + ��. �� = ��. �� ��

#�$%�&��� � = &'�(� �. ��� = ��. �

(ii) At the maximum height the velocity is zero, then;

��� = ���� + �'∆�

= �. �� + �(−�. ��)∆�

∆� = ��. ����. "� = �. �� �

(iii) When the ball returns to the ground the vertical displacement is zero, thus;

∆� = ���& + �� '&�

= �. �& − �. ��� &�

& = �. ����. �� = �. �" �

(iv) Horizontal range x = vx t = 41 x 1.86 = 76.26 m

(2) A boy kicks a ball so it should go over a wall 2 meters high and 5 meters away from him. What

should be the initial velocity of the ball?

Solution:

At the top of the wall the vertical velocity is zero, then;

��� = �� �� �� + �'∆�

= (������)� − ���. ����

������ = √��. �� = ". �" �/�

To find the time taken to reach the top of the wall we use the equation

�� = ������ + '&

= ". �" − �. ��&

Then t = 0.64 s

� = ������ &

= (������). "�

������ = . "� = �. � �/�

��� = ". �"� + �. �� = �. �

�� = � �/�

#�$%�&��� � = &'�(� ". �"�. � = ��. ��

3- A box of supplies is dropped from an airplane flying horizontally with a speed of 330 km/h at a

height of 30 km. Calculate:

(i) The time it takes the box to reach the ground.

(ii) The velocity of the box when it hits the ground

(iii) The horizontal displacement of the box

Solution:

Initially the box has velocity components along the y-axis equal to zero, and an x-component equal to

330 km/h

��� = '�# ��� = �� ,�- = ��. "� �/� (i) ∆� = ���& + �� '&�

−� = − �. ��� &�

& = .����. �� = "��". � �

(ii) ��� = ���� + �'∆�

��� = + �(−�. ��)(−�)

�� = √��" = �"�. � �/�

|�| = √��" + ���. � = ���. � �/�

#�$%�&��� � = &'�(� �"�. ���. "� = ��. �� /%0�1 &-% -�$�2��

(iii) The horizontal displacement = x = vx t = 91.67 x 6116.2 = 560672.1 m