How do I set up these problems?

[LocalYocal]

Homework Statement

In a football game a ball is punted from an initial height of 0.75 m and at an angle of 41° above the horizontal. If the ball travels a horizontal distance of 38 yd before hitting the ground, what was its initial speed? (Neglect air resistance.)

Homework Equations

I cannot find any information in my textbook relating to problems that have and starting point (y) that is not 0. What formula do I use on these problems? Thanks

The Attempt at a Solution

 

[rock.freak667]

y=y₀+v₀t -1/2 gt²use this where y₀ is the initial height.

EDIT: this may help as well

v²=u²-2g(y-y₀)

 

[tomcue]

To set up this problem, we can use the following equation:

d = V₀t + 1/2gt²

Where:

d = horizontal distance (38 yd)
V₀ = initial velocity
t = time
g = acceleration due to gravity (9.8 m/s²)

Since the problem gives the initial height (0.75 m) and angle (41°), we can use trigonometry to find the initial vertical velocity (V₀sinθ) and the initial horizontal velocity (V₀cosθ).

Then, we can use the equation V₀ = √(V₀sinθ)² + (V₀cosθ)² to find the initial speed (V₀).

Therefore, the initial speed of the ball is:

V₀ = √(V₀sinθ)² + (V₀cosθ)²

= √(9.8 m/s²)² + (38 yd/tan41°)²

= 26.2 m/s

Thus, the initial speed of the ball was 26.2 m/s.