Answer:
1.697s
Explanation:
We use the second equation of free fall under gravity as follows;
[tex]h=ut+\frac{1}{2}gt^2...............(1)[/tex]
Since the ball fell freely, u = 0m/s, therefore equation (1) reduces to
[tex]h=\frac{1}{2}gt^2...............(2)[/tex]
Given that h is the total height the ball falls through in time t seconds.
However, according to the stated problem the ball falls halfway in 1.2s, this simply implies that the ball falls through a distance of [tex]\frac{h}{2}[/tex] in 1.2s. Hence we can write the following, given that [tex]g=9.8m/s^2[/tex];
[tex]\frac{h}{2}=\frac{1}{2}*9.8*1.2^2\\hence\\h=9.8*1.2^2\\h=14.112m[/tex]
We can now proceed to find the time t for which it falls through h = 14.112m as follows;
[tex]14.112=\frac{1}{2}*9.8*t^2\\14.112=4.9t^2\\t^2=\frac{14.112}{4.9}\\t^2=2.88\\t=\sqrt{2.88} \\t=1.697s[/tex]
The time it takes for the ball to fall from rest all the way to the ground is ≈ 1.7 secs
First step : determine the distance ( h ) travelled by the wrecking ball halfway
h = ut + 1/2 gt^2 ---- ( 1 )
where velocity at rest ( u ) = 0
g ( acceleration due to gravity ) = 9.8 m/s^2
t = 1.2 secs .
back to equation 1
h = 0 + 1/2 ( 9.8 * 1.2^2 )
= 0 + 1/2 * 14.112 = 7.056 m
∴ Total distance travelled ( H ) by the wrecking ball = 7.056 * 2 = 14.112 m
finally determine the time it takes for the ball to fall from rest all the way to the ground
H = ut + 1/2 gT^2 ---- ( 2 )
14.112 = 0 + 1/2 ( 9.8 * T^2 )
∴ T = √ ( 14.112 * 2 ) / 9.8
= √2.88 = 1.697 ≈ 1.70 secs
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