Physics Motion in Plane

A person can throw a ball upto a maximum range of 100m. How high above the ground he can the same ball?

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alok kumar singh

Contributor-Level 10

According to question, we can write

$R = \frac{u^{2} s i n 2 θ}{g} \Rightarrow u^{2} = g R_{m a x}, w h e r e θ = 45 °$

$\Rightarrow H_{m a x} = \frac{u^{2}}{2 g} = \frac{g R_{m a x}}{2 g} = \frac{R_{m a x}}{2} = \frac{100}{2} = 50 m$

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2 months ago

An electron in a research apparatus follows a circle path. On the electron's first circuit of the apparatus, its speed is v₀ and the radius of its circular path is R. Each time it makes on circuit, it passes a short region where it receives a “kick” and gains an additional speed of $\frac{v_{0}}{100} .$ The electron follows a circular path such that the magnitude of its acceleration is always the same. What is the radius of the circular path after the electron has received 10 kicks?

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Contributor-Level 10

$a = \frac{v_{0}^{2}}{R}$ $\frac{_{}^{}}{}$

after 10 kicks, $v = v_{0} + \frac{10 v_{0}}{100} = 1.1 v_{0}$ $_{} \frac{_{}}{}_{}$

$\Rightarrow R_{1} = 1.21 R$

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2 months ago

A projectile travels at θ below horizontal 1 sec after projection as shown. What is the value of θ?

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Contributor-Level 10

$t a n θ = \frac{v_{y}}{v_{x}} = \frac{u_{y} - g t}{u_{x}}$

$\Rightarrow t a n θ = | \frac{8 - 10}{4} | = | - \frac{1}{2} |$

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2 months ago

Two particles start moving from the same point in two different directions. The first particle moves along the positive x-axis with a constant acceleration of 3 m/s². The second particle moves in a straight line making an angle of 60° with the positive x-axis with a constant speed of 24 m/s. Find the time after which the relative velocity of the particles is minimum.

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Contributor-Level 10

v? = 3tî v? = 24cos 60°î + 24sin 60°? = 12î + 12√3?
v? = v? – v? = (12 – 3t)î + 12√3?
It is minimum when 12 - 3t = 0 ⇒ t = 4sec

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2 months ago

A particle is moving in a circle of radius 1m with angular velocity (ω) given as a function of angular displacement ( θ ) by the relation ω = θ² + 2θ. The total acceleration of the particle when θ = 1rad is:

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Contributor-Level 10

ω = θ² + 2θ
α = (ωdω)/dθ = (θ² + 2θ) (2θ + 2)
At θ = 1rad.
ω = 3rad/s and α = 12rad/s²
a? = αR = 12 m/s² a? = ω²R = 9 m/s² A? = √ (a? ² + a? ²) = 15 m/s²

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2 months ago

Which one of the following relations is true for two unit vector $\hat{A} a n d \hat{B}$ making an angle to each other?

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Raj Pandey

Contributor-Level 9

$| \hat{A} + \hat{B} | = \sqrt[]{A^{2} + B^{2} + 2 A B c o s θ}$

$= \sqrt[]{1 + 1 + 2 c o s θ}$

$= \sqrt[]{2 (1 + c o s θ)}$

= $\sqrt[]{2 * 2 c o s^{2} \frac{θ}{2}}$

$| \hat{A} + \hat{B} | = 2 c o s \frac{θ}{2}$ -(1)

$| \hat{A} - \hat{B} | = \sqrt[]{A^{2} + B^{2} - 2 A B c o s θ}$

$= \sqrt[]{1 + 1 - 2 c o s θ}$

$= 2 s i n \frac{θ}{2}$ -(2)

(2) $\div$ (1)

$\frac{| \hat{A} - \hat{B} |}{| \hat{A} + \hat{B} |} = \frac{2 s i n \frac{θ}{2}}{2 c o s \frac{θ}{2}}$

$\Rightarrow | \hat{A} - \hat{B} | = | \hat{A} + \hat{B} | t a n \frac{θ}{2}$

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2 months ago

$\vec{A}$ is a vector quantity such that $| \vec{A} |$ = non-zero constant. Which of the following expression is true for $\vec{A}$ ?

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Raj Pandey

Contributor-Level 9

$\vec{A} * \vec{A} = A A s i n θ \hat{n}$

$= A A s i n 0 ° \hat{n}$

= 0 [since Angle between the vectors are zero degree]

$\vec{A} * \vec{A} = 0$

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2 months ago

A grass hopper can jump maximum distance 1.6 m. It spends negligible time on ground. How far can it go in 2√2s (in meters)?

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Contributor-Level 10

Maximum range is obtained at 45?
u²/g = 1.6 or u = 4m/s
T = (2u sin 45? )/g = (2*4* (1/√2)/10 = 0.4√2s
Number of jumps in a given time, n = t/T = 2√2 / 0.4√2 = 5

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2 months ago

A flying disc of radius r is moving with constant speed v? while rotating anticlockwise with angular speed v?/r along a curve PQ as shown below. Radius of curvature of curve at the instant is 4r. The magnitude of acceleration of point A at the instant is (3v₀²)/(nr). Find n.

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Contributor-Level 10

a? = v? ²/4r
a_A? = (v? ²/r²) * r = v? ²/r
a_A = 3v? ²/4r

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2 months ago