To solve this problem, we need to consider the motion of the golf ball in both the vertical and horizontal
directions separately.
Given:
Initial velocity (v₀) = 4.35 m/s
Launch angle (θ) = 81 degrees above the horizontal
We can break down the initial velocity into its vertical and horizontal components:
Vertical component: v₀ * sin(θ)
Horizontal component: v₀ * cos(θ)
Since there is no horizontal acceleration (assuming no air resistance), the time it takes for the ball to
land will be the same as the time it takes for the ball to reach its maximum height (assuming the ground
is at the same level as the initial position).
To find the time taken for the ball to reach its maximum height, we can use the vertical component of
the initial velocity and the acceleration due to gravity.
Vertical component (vₑ) = v₀ * sin(θ)
Acceleration due to gravity (g) = 9.8 m/s² (assuming no air resistance)
The time taken to reach maximum height (t₁) can be found using the formula:
vₑ = v₀ + (g * t₁)
Solving for t₁:
t₁ = (vₑ - v₀) / g
Once the ball reaches its maximum height, it will fall back to the ground. The time taken to reach the
ground from the maximum height will be the same as the time taken to reach the maximum height.
Therefore, the total time taken for the ball to land will be:
t_total = 2 * t₁
Let's calculate the values:
Vertical component (vₑ):
vₑ = v₀ * sin(θ) = 4.35 m/s * sin(81°)
Horizontal component:
v₀ * cos(θ) = 4.35 m/s * cos(81°)
Now we can calculate t₁ and t_total:
t₁ = (vₑ - v₀) / g
t_total = 2 * t₁
Substituting the values, we can find the solution.