Page 19 - Pra U STPM 2021 Penggal 1 - Physics

Physics Term 1 STPM Chapter 2 Kinematics

Example 7

An aircraft flies at a height h with a constant horizontal velocity u so as to fly over a cannon. When
the aircraft is directly over the cannon, a shot is fired to hit the aircraft. Neglecting air resistance,
find in terms of u, h and g, the acceleration due to gravity the minimum speed of the shell in order
to hit the aircraft.
2
Solution:
v
If v = minimum speed
θ = angle of projection u
With this minimum speed, the shell hits the aircraft at the maximum h
height reached by the shell, and since the shell is fired when the air- θ
craft is above the cannon,
horizontal component of shell velocity = speed of aircraft, u
v cos θ = u .............................. ①
v sin θ
2
2
Using maximum height, h =
2g
2
2
v sin θ = 2gh .............................. ②
2
2
① + ②: v sin θ + v cos θ = 2gh + u 2
2
2
v = u + 2gh
2
Example 8
The diagram shows the path of a bullet fired 20.0 m s –1
horizontally with a velocity of 20.0 m s from a
–1
height of 2.0 m. Calculate
(a) the speed of the bullet v, 2.0 m
(b) the angle θ when the bullet hits the ground.
v
θ
Solution:

The horizontal component of velocity v x = 20.0 m s (constant)
–1
To find the vertical component of velocity when the bullet hit the ground, consider vertical
component of motion:

Initial vertical component of velocity = 0
Acceleration, a = g
Vertical displacement, s = 2.0 m
1
Using s = ut + at 2
2
1
2.0 = 0 + × 9.81 × t 2
2
t = 0.639 s

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