A stone is projected vertically upwards with | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For the first stone projected vertically upwards,the maximum height reached is $h_1 = \frac{v^2}{2g}$.The potential energy at the highest point is

Vedclass · Accepted Answer

$4:1$

Vedclass · Answer

(A) For the first stone projected vertically upwards,the maximum height reached is $h_1 = \frac{v^2}{2g}$.The potential energy at the highest point is $PE_1 = mgh_1 = mg \left( \frac{v^2}{2g} ight) = \frac{mv^2}{2}$.For the second stone,the angle with the vertical is $60^{\circ}$,which means the angle with the horizontal is $	heta = 90^{\circ} - 60^{\circ} = 30^{\circ}$.The maximum height reached by the second stone is $h_2 = \frac{v^2 \sin^2 	heta}{2g} = \frac{v^2 \sin^2 30^{\circ}}{2g} = \frac{v^2 (0.5)^2}{2g} = \frac{v^2}{8g}$.The potential energy at the highest point is $PE_2 = mgh_2 = mg \left( \frac{v^2}{8g} ight) = \frac{mv^2}{8}$.The ratio of their potential energies is $\frac{PE_1}{PE_2} = \frac{mv^2/2}{mv^2/8} = \frac{8}{2} = 4:1$.

Column-$I$	Column-$II$
$(1)$ Vertical component of velocity is zero	$(a)$ Tangent to the parabolic path
$(2)$ Linear velocity	$(b)$ Maximum height point of the projectile trajectory

Similar Questions

$A$ particle covers $50\, m$ distance when projected with an initial speed. On the same surface,it will cover a distance of ......... $m$ when projected with double the initial speed.

Assertion $(A)$: The range of a projectile is maximum when the angle of projection is $45^{\circ}$.
Reason $(R)$: The range of a projectile depends only on the angle of projection.

Match Column-$I$ with Column-$II$.

Column-$I$ Column-$II$

$(1)$ Vertical component of velocity is zero $(a)$ Tangent to the parabolic path

$(2)$ Linear velocity $(b)$ Maximum height point of the projectile trajectory

In a sports competition,a javelin is thrown at an angle $45^{\circ}$,which recorded a range of $90 \,m$. The maximum height reached by the javelin is (Neglect air resistance and acceleration due to gravity $g = 10 \,ms^{-2}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module