Solve Proportionality Problem: Find Golf Ball Height When Speed is 35 m/s

Question

A golf ball, thrown upwards, rises at a speed of v metres per second. The ball reaches a maximum height of h metres. h is proportional to the square of v. When v = 20, h = 8. Work out the maximum height reached by the golf ball when v = 35.

Accepted Answer

24.5

Answer

Step 1: Translate the proportional relationship into an equation. Since h is proportional to the square of v, we write this as $h = kv^2$, where $k$ is the constant of proportionality. Step 2: Calculate the value of $k$ using the given values $v=20$ and $h=8$. Substitute into the equation: $8 = k \times (20)^2$. Simplify $20^2$ to 400, so $8 = 400k$. Solve for $k$ by dividing both sides by 400: $k = 8/400 = 0.02$. Step 3: Use the constant $k$ to find $h$ when $v=35$. Substitute $v=35$ and $k=0.02$ into the equation $h = kv^2$: $h = 0.02 \times (35)^2$. Calculate $35^2 = 1225$, then multiply by 0.02: $h = 0.02 \times 1225 = 24.5$.