An object is thrown vertically upward with an initial velocity of 10 m/sec from a height of 3 meters. In meters, find the highest point it reaches. (Round your answer to three decimal places.) m Find when it hits the ground. (Enter your answer in seconds. Round your answer to three decimal places.) s

a) 8.1 m

b) 2.306 s

Explanation:

To calculate the highest vertical distance travelled, we will Use the equations of motion,

u = initial velocity of the object = 10 m/s

v = velocity of the object at maximum height reached (the vertex) = 0 ft/s

y = highest vertical height reached = ?

y₀ = initial height of the object = 3 m

g = acceleration due to gravity = -9.8 m/s²

v² = u² + 2g(y - y₀)

0² = 10² + (2)(-9.8)(y - 3)

(y - 3) = 100/(2×9.8)

y - 3 = 5.102

y = 5.102 + 3 = 8.102 m

b) For the time taken for the object to hit the ground.

We will calculate the time taken to reach maximum height and add it to the time to reach the ground from maximum height.

Time taken to reach maximum height

u = initial velocity of the object = 10 m/s

v = velocity of the object at maximum height reached = 0 m/s

g = acceleration due to gravity = -9.8 m/s²

t₁ = ?

v = u + gt₁

0 = 10 + (-9.8)t₁

t₁ = (10/9.8)

t₁ = 1.02 s

Time taken to reach the ground from maximum height

u = initial velocity of the object at maximum height = 0 m/s

t₂ = ?

y = 8.102 m

g = acceleration due to gravity = 9.8 ft/s²

y = ut + (1/2)gt₂²

8.102 = 0 + (1/2)(9.8)t₂²

t₂² = (2×8.102)/9.8

t₂² = 1.653

t₂ = 1.286 s

T = t₁ + t₂ = 1.020 + 1.286

T = 2.306 s

Hope this Helps!!!

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