Question 3: Motion in 1D

Question

In an experiment to measure the height of a bridge by dropping stone into water underneath. If the error in measurement of time is $$0.2 \mathrm{~s}$$ at the end of $$4 \mathrm{~s}$$, then the error in estimation of height of bridge will be (neglect the water resistance, i.e. thrust)

Accepted Answer

We have
$$S=u t+\frac{1}{2} a t^2$$
$$\begin{aligned}
	ext{or} \quad h & =(0) t+\frac{1}{2} 	imes 9.8 	imes(4)^2 \quad\left(\begin{array}{l}
\because a=g \
\because u=0
\end{array}ight) \
& =78.4 \mathrm{~m}
\end{aligned}$$
$$\begin{gathered}
	ext{Given,} \quad \Delta t=0.2 \mathrm{~s} \
t=4 \mathrm{~s}
\end{gathered}$$
Now, for error
$$\frac{\Delta h}{h}= \pm 2\left(\frac{\Delta t}{t}ight)= \pm 2\left(\frac{0.2}{4}ight)= \pm 0.1$$
$$\begin{aligned}
	ext{or} \quad \Delta h & = \pm 0.1 	imes h \
& = \pm 0.1 	imes 78.4= \pm 7.84 \mathrm{~m}
\end{aligned}$$

Answer

$$\pm 19.68 \mathrm{~m}$$

Answer

$$\pm 17.22 \mathrm{~m}$$

Answer

$$\pm 7.84 \mathrm{~m}$$

Answer

$$\pm 12.22 \mathrm{~m}$$

Motion in 1D

In an experiment to measure the height of a bridge by dropping stone into water underneath. If the error in measurement of time is $0.2 \mathrm{~s} at the end of 4 \mathrm{~s}$, then the error in estimation of height of bridge will be (neglect the water resistance, i.e. thrust)

Choose the correct answer: