Answer:
1. Speed=0
2. 2.46 s
3.30.1 m
4. 22.0 m
5.1.004 s
Explanation:
We are given that
Initial speed of blue ball, u=24.1 m/s
Height of blue ball from ground y_0=0.5 m
Initial speed of red ball , u'=7.2 m/s
Height of red from ground=y'0=32 m
Gravity, g=[tex]9.81ms^{-2}[/tex]
1.When the ball reaches its maximum height then the speed of the blue ball is zero.
2.v=0
[tex]v=u+at[/tex]
Using the formula and substitute the values
[tex]0=24.1-9.81t[/tex]
Where g is negative because motion of ball is against gravity
[tex]24.1=9.81t[/tex]
[tex]t=\frac{24.1}{9.81}=2.46s[/tex]
3.[tex]y=y_0+ut+\frac{1}{2}at^2[/tex]
Using the formula
[tex]y=0.5+24.1(2.46)-\frac{1}{2}(9.81)(2.46)^2[/tex]
[tex]y=30.1 m[/tex]
4.Time of flight for red ball=3.77-2.9=0.87s
[tex]y'=32-7.2(0.87)-\frac{1}{2}(9.81)(0.87)^2[/tex]
[tex]y'=22.0m[/tex]
Hence, the height of red ball 3.77 s after the blue ball is 22.0 m.
5.According to question
[tex]0.5+24.1(t+2.9)-\frac{1}{2}(9.81)(2.9+t)^2=32-7.2t-\frac{1}{2}(9.81)t^2[/tex]
[tex]0.5+24.1t+69.89-4.905(t^2+5.8t+8.41)=32-7.2t-4.905t^2[/tex]
[tex]0.5+24.1t+69.89-4.905t^2-28.449t-41.25105=32-7.2t-4.905t^2[/tex]
[tex]0.5+69.89-41.25105-32=-24.1t+28.449t-7.2t[/tex]
[tex]-2.86105=-2.851t[/tex]
[tex]t=\frac{2.86105}{2.851}=1.004 s[/tex]
Hence, 1.004 s after the blue ball is thrown are the two balls in the air at the same height.
