When a stone is thrown upwards with an initial velocity of v metres per second, it reaches a maximum height of h metres.
h is directly proportional to the square of v.
Calculate the value of v when h = 50
Please help
Your answer is wrong
To solve this problem, we can use the concept of direct proportion. Let me explain step-by-step how to find the value of v when h = 50.
1. Understand the problem: We know that h is directly proportional to the square of v. This means that if we double v, h will quadruple (increase by a factor of 4), and if we halve v, h will be reduced to one-fourth (decrease by a factor of 1/4).
2. Set up the proportion: Since h is directly proportional to the square of v, we can write the proportion as:
h₁ / v₁² = h₂ / v₂²
Where h₁ and v₁ are the original height and velocity, and h₂ and v₂ are the new height and velocity. In this case, we know h₁ = 50, and we want to find v₂ when h₂ = 50.
3. Solve the proportion: Plug in the values:
50 / v₁² = 50 / v₂²
since h₁ = h₂ = 50.
4. Simplify the equation: Cancel out the common factor of 50:
1 / v₁² = 1 / v₂²
5. Solve for v₂: Cross-multiply the equation:
v₂² = v₁²
Take the square root of both sides:
v₂ = v₁
Since we want to find v₂ when h₂ = 50, we can conclude that v = 50.
Therefore, the value of v when h = 50 is 50 meters per second.
y = vt - 4.9t^2
max height h is at t = v/9.8, so
h = v^2/19.6
v^2 = 50*19.6
v = 31.3 m/s