A ball is thrown vertically upwards with a speed of 30 m/s. What is the maximum height it reaches? (g = 9.8 m/s²)
Practice Questions
1 question
Q1
A ball is thrown vertically upwards with a speed of 30 m/s. What is the maximum height it reaches? (g = 9.8 m/s²)
45.9 m
46.0 m
46.1 m
46.2 m
Using conservation of energy, initial kinetic energy = potential energy at maximum height. 0.5mv² = mgh. Solving gives h = v²/(2g) = (30)²/(2 * 9.8) = 45.9 m.
Questions & Step-by-step Solutions
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Q
Q: A ball is thrown vertically upwards with a speed of 30 m/s. What is the maximum height it reaches? (g = 9.8 m/s²)
Solution: Using conservation of energy, initial kinetic energy = potential energy at maximum height. 0.5mv² = mgh. Solving gives h = v²/(2g) = (30)²/(2 * 9.8) = 45.9 m.
Steps: 10
Step 1: Understand that when the ball is thrown upwards, it has initial speed and will rise until it stops momentarily at the maximum height.
Step 2: Recognize that at the maximum height, all the initial kinetic energy (energy of motion) will be converted into potential energy (stored energy due to height).
Step 3: Write down the formula for kinetic energy: KE = 0.5 * m * v², where m is mass and v is initial speed (30 m/s).
Step 4: Write down the formula for potential energy at maximum height: PE = m * g * h, where g is the acceleration due to gravity (9.8 m/s²) and h is the height we want to find.
Step 5: Set the initial kinetic energy equal to the potential energy at maximum height: 0.5 * m * v² = m * g * h.
Step 6: Notice that the mass (m) cancels out from both sides of the equation, simplifying it to: 0.5 * v² = g * h.
Step 7: Rearrange the equation to solve for height (h): h = v² / (2 * g).
Step 8: Substitute the values into the equation: h = (30)² / (2 * 9.8).
Step 9: Calculate (30)² = 900, and then calculate 2 * 9.8 = 19.6.
Step 10: Divide 900 by 19.6 to find h: h = 900 / 19.6 ≈ 45.9 m.
