Find the value of kk for which the constant function x(t)=kx(t)=k is a solution of the differential equation 3t3dxdt+5x−3=03t3dx
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Answer:
The ball will take 6.3 seconds to reach the maximum height and hit the ground.
Step-by-step explanation:
a). When a ball was thrown upwards with an initial velocity u then maximum height achieved h will be represented by the equation
v² = u² - 2gh
where v = final velocity at the maximum height h
and g = gravitational force
Now we plug in the values in the equation
At maximum height final velocity v = 0
0 = (28)² - 2×(9.8)h
19.6h = (28)²
h =
=
= 40 meter
B). If the ball misses the building and hits the ground then we have to find the time after which the ball hits the ground that will be
= Time to reach the maximum height + time to hit the ground from the maximum height
Time taken by the ball to reach the maximum height.
Equation to find the time will be v = u - gt
Now we plug in the values in the equation
0 = 28 - 9.8t
t =
= 2.86 seconds
Now time taken by the ball to hit the ground from its maximum height.
H = ut +
(17 + 40) = 0 +
57 = 4.9(t)²
t² =
t² = 11.63
t = √(11.63)
= 3.41 seconds
Now total time taken by the ball = 2.86 + 3.41
= 6.27 seconds
≈ 6.3 seconds
Therefore, the ball will take 6.3 seconds to reach the maximum height and hit the ground.
