Two bodies are thrown with the same initial speed at angles α and 90 ∘ - α with the horizontal. What will be horizontal ranges?

Given, Initial speed = R 1 = R 2 Angle of Range 1 = α Angle of Range 2 = 90 - α We know the formula of range in a projectile is Range = u 2 sin 2 θ g So ratio in both case, R 1 R 2 = sin 2 α sin 2 90 ° - α = sin 2 α sin 180 ° - α = sin 2 α sin 2 α = 1 So, R 1 = R 2 Hence, it is the required answer.

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What is point mass give examples?

Important Questions on Motion and Measurement of Distance

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Science>Physics>Motion and Measurement of Distance>Rest and Motion

Motion of a particle in

x - y

plane is described by a set of following equations

x = 4 \sin (\frac{π}{2} - ω t) m

and

y = 4 \sin (ω t) m

. The path of the particle will be

HARD

Science>Physics>Motion and Measurement of Distance>Rest and Motion

Three balls, $A, B$ and $C$ are released and all reach the point $X$ (shown in the figure). Balls $A$ and $B$ are released from two identical structures, one kept on the ground and the other at height $h$ from the ground as shown in the figure. They take time $t_{A}$ and $t_{B}$ respectively to reach $X$ (time starts after they leave the end of the horizontal portion of the structure). The ball $C$ is released from a point at height $h$ vertically above $X$ and reaches $X$ in time $t_{C}$ . Choose the correct statement.

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MEDIUM

Science>Physics>Motion and Measurement of Distance>Rest and Motion

When a particle moves with variable velocity, which of the following statement are NOT correct ?
(i) Average speed = average velocity
(ii) Instantaneous speed = instantaneous velocity
(iii) Distance covered = magnitude of displacement

EASY

Science>Physics>Motion and Measurement of Distance>Rest and Motion

Starting at time

t = 0

from the origin with speed

1 m s^{- 1}

, a particle follows a two-dimensional trajectory in the

x - y

plane so that its coordinates are related by the equation

y = \frac{x^{2}}{2}

. The

x

and

y

components of its acceleration are denoted by

a_{x}

and

a_{y}

, respectively. Then

MEDIUM

Science>Physics>Motion and Measurement of Distance>Rest and Motion

Two skaters, $P$ and $Q$ are skating towards each other. Skater, $P$ throws a ball towards, $Q$ every $5 s$ such that it always leaves her hand with speed $2 m s^{- 1}$ with respect to the ground. Consider two cases: (I) $P$ runs with speed $1 m s^{- 1}$ towards $Q,$ while $Q$ remains stationary. (II) $Q$ runs with speed $1 m s^{- 1}$ towards $P,$ while $P$ remains stationary. Note That irrespective of speed of $P,$ ball always leaves $P$ s hand with speed $2 m s^{- 1}$ with respect to the ground. Ignore gravity. Balls will be received by $Q .$

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Science>Physics>Motion and Measurement of Distance>Rest and Motion

What are different types of motions?

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Science>Physics>Motion and Measurement of Distance>Rest and Motion

A person sitting in an open car moving at a constant velocity throws a ball vertically up into the air. The ball falls

MEDIUM

Science>Physics>Motion and Measurement of Distance>Rest and Motion

Two bodies are thrown with the same initial speed at angles

α

and

(90^{\circ} - α)

with the horizontal. What will be horizontal ranges?

HARD

Science>Physics>Motion and Measurement of Distance>Rest and Motion

A child runs to and fro with a speed $9 km h^{- 1}$ (with respect to the belt) on a long horizontally moving belt (figure) between $h$ is father and mother located $50 m$ apart on the moving belt. The belt moves with a speed of $4 km h^{- 1}$ . For an observer on the stationary platform outside, what is the $(a)$ speed of the child running in the direction of motion of the belt and $(b)$ speed of the child running opposite to the direction of motion of the belt? $(c)$ time taken by the child in $(a)$ and $(b)$ . Which of the answers will alter if motion is viewed by one of the parents?