Question:
A ball is thrown vertically upward with a speed of \(19.6\ \text{m/s}\). The value of acceleration due to gravity at that place is \(9.8\ \text{m/s}^2\). The maximum height (in cm) that the ball reaches is _ _ _. (in integer)
A ball is thrown vertically upward with a speed of \(19.6\ \text{m/s}\). The value of acceleration due to gravity at that place is \(9.8\ \text{m/s}^2\). The maximum height (in cm) that the ball reaches is _ _ _. (in integer)
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At the maximum height of vertical motion, the final velocity becomes zero. Use:
\[
v^2=u^2-2gh
\]
to calculate the height reached.
Updated On: Jun 5, 2026
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Verified By Collegedunia
Correct Answer: 1960
Solution and Explanation
Step 1: Write the given quantities.
Initial velocity:
\[ u=19.6\ \text{m/s} \] Acceleration due to gravity:
\[ g=9.8\ \text{m/s}^2 \] At maximum height, final velocity becomes
\[ v=0 \]
Step 2: Use the equation of motion.
The kinematic equation is
\[ v^2=u^2-2gh \] where \(h\) is the maximum height.
Step 3: Substitute the known values.
\[ 0=(19.6)^2-2(9.8)h \]
Step 4: Simplify the equation.
\[ (19.6)^2=384.16 \] Thus,
\[ 384.16=19.6h \]
Step 5: Solve for height.
\[ h=\frac{384.16}{19.6} \] \[ h=19.6\ \text{m} \]
Step 6: Convert meters into centimeters.
\[ 1\ \text{m}=100\ \text{cm} \] Therefore,
\[ 19.6\ \text{m}=19.6\times 100 \] \[ =1960\ \text{cm} \]
Step 7: Final conclusion.
Hence, the maximum height reached by the ball is
\[ \boxed{1960} \]
Initial velocity:
\[ u=19.6\ \text{m/s} \] Acceleration due to gravity:
\[ g=9.8\ \text{m/s}^2 \] At maximum height, final velocity becomes
\[ v=0 \]
Step 2: Use the equation of motion.
The kinematic equation is
\[ v^2=u^2-2gh \] where \(h\) is the maximum height.
Step 3: Substitute the known values.
\[ 0=(19.6)^2-2(9.8)h \]
Step 4: Simplify the equation.
\[ (19.6)^2=384.16 \] Thus,
\[ 384.16=19.6h \]
Step 5: Solve for height.
\[ h=\frac{384.16}{19.6} \] \[ h=19.6\ \text{m} \]
Step 6: Convert meters into centimeters.
\[ 1\ \text{m}=100\ \text{cm} \] Therefore,
\[ 19.6\ \text{m}=19.6\times 100 \] \[ =1960\ \text{cm} \]
Step 7: Final conclusion.
Hence, the maximum height reached by the ball is
\[ \boxed{1960} \]
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