Answer:
a) After 5.19 seconds dog catch the ball.
b) From the dog's initial position at 20.20 m dog catches the ball.
c) Speed of the ball when dog catches ball = 2.405 m/s
Speed of the dog when dog catches ball = 7.785 m/s
Explanation:
a) Let the time of catching be t.
We have equation of motion s = ut + 0.5 at²
Consider the motion of ball
Initial velocity, u = 5 m/s
Acceleration, a = -0.5 m/s²
Time, t = t
Substituting
s = 5 x t + 0.5 x -0.5 x t²
s = 5t - 0.25t²
Consider the motion of dog
Initial velocity, u = 0 m/s
Acceleration, a = 1.5 m/s²
Time, t = t
Substituting
s + 1 = 0 x t + 0.5 x 1.5 x t²
s = 0.75t²
If they catch up displacement of dog is 1 m more than displacement of ball.
That is
5t - 0.25t² + 1 = 0.75t²
t² - 5t -1 = 0
t = 5.19 or t = -0.19(not possible)
So after 5.19 seconds dog catch the ball.
b) Displacement of dog, s = 0.75t²
s = 0.75 x 5.19²
s = 20.20 m
From the dog's initial position at 20.20 m dog catches the ball.
c) We have equation of motion v = u + at
Consider the motion of ball
Initial velocity, u = 5 m/s
Acceleration, a = -0.5 m/s²
Time, t = 5.19 s
Substituting
v = 5 + -0.5 x 5.19 = 2.405 m/s
Speed of the ball when dog catches = 2.405 m/s
Consider the motion of dog
Initial velocity, u = 0 m/s
Acceleration, a = 1.5 m/s²
Time, t = 5.19 s
Substituting
v = 0 + 1.5 x 5.19 = 7.785 m/s
Speed of the dog when dog catches ball = 7.785 m/s
