Answer:
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!!!