Subjective Type

A small ball rolls horizontally off the edge of a tabletop that is $$1.20 m$$ high. It strikes the floor at a point $$1.52 m$$ horizontally from the table edge. (a) How long is the ball in the air? (b) What is its speed at the instant it leaves the table?

Solution

We adopt the positive direction choices used in the textbook so that equations such as

(a) With the origin at the initial point (edge of table), the $$y$$ coordinate of the ball is given
by $$yy=-\frac { 1 }{ 2 } g{ t }^{ 2 }$$. If $$t$$ is the time of flight and $$y = –1.20 m$$ indicates the level at which the all hits the floor, then
$$t=\sqrt { \frac { 2(-1.20m) }{ -9.80m/{ s }^{ 2 } } } =0.495s.$$
(b) The initial (horizontal) velocity of the ball is $$\vec { v } ={ v }_{ 0 }\hat { i. } $$. Since $$x = 1.52 m$$ is the horizontal position of its impact point with the floor, we have $$x = { v }_{ 0 }t$$. Thus,
$${ v }_{ 0 }=\frac { x }{ t } =\frac { 1.52m }{ 0.495s } =3.07m/{ s }.$$

SIMILAR QUESTIONS

Kinematics

A particle of mass $$m$$ and charge $$q$$ is released from rest at the origin as shown in the figure. The speed of the particle when it has travelled a distance $$d$$ along the z-axis is given by:-

Kinematics

In a two dimensional motion, instantaneous speed $$ { v }_{ 0 } $$ is a positive constant. Then which of the following are necessarily true?

Kinematics

In one dimensional motion, instantaneous speed $$v$$ satisfies the condition, $$ 0 \leq v < v_0$$,when

Kinematics

You pull a short refrigerator with a constant force across a greased (frictionless) floor,either with horizontal (case 1) or with tilted upward at an angle u(case 2).(a)What is the ratio of the refrigerator’s speed in case 2 to its speed in case 1 if you pull for a certain time t? (b) What is this ratio if you pull for a certain distance d?

Kinematics

A cyclist turns around a curve at 15 miles/hour. If he turns at double the speed, the tendency to overturn is

Kinematics

The coordinates of a moving particle at any time $$t$$ are given by $$x=c{ t }^{ 2 }$$ and $$y=b{ t }^{ 2 }$$. Then the speed of the particle is given by

Kinematics

The numerical value of ratio of instantaneous velocity to instantaneous speed is

Kinematics

Linear velocity of the $$CM$$ of rod is

Kinematics

A particle moving with an initial velocity $$ \hat { i } -4\hat { j } +10\hat { k } $$ has acceleration $$ \hat { i } +\hat { j } -2\hat { k } $$. Its velocity at the end of 2 seconds, points along the unit vector:

Contact Details