A bowling machine placed at a height h above | vedclass

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

Question

(D) For a projectile launched horizontally from a height $h$ with initial velocity $u = 10 \sqrt{3} 	ext{ m s}^{-1}$:$1$. The horizontal component of

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(D) For a projectile launched horizontally from a height $h$ with initial velocity $u = 10 \sqrt{3} 	ext{ m s}^{-1}$:$1$. The horizontal component of velocity remains constant: $v_x = u = 10 \sqrt{3} 	ext{ m s}^{-1}$.$2$. The vertical component of velocity at the time of landing is $v_y = \sqrt{2gh}$.$3$. The angle $	heta$ that the velocity vector makes with the horizontal is given by $	an 	heta = \frac{v_y}{v_x}$.$4$. Given that the landing angle is $30^{\circ}$ or more,we have $	an 	heta \geq 	an 30^{\circ}$.$5$. Substituting the values: $\frac{\sqrt{2gh}}{10 \sqrt{3}} \geq \frac{1}{\sqrt{3}}$.$6$. Simplifying: $\sqrt{2gh} \geq 10$.$7$. Squaring both sides: $2gh \geq 100$.$8$. With $g = 10 	ext{ m s}^{-2}$,we get $20h \geq 100$,which implies $h \geq 5 	ext{ m}$.$9$. The minimum height is $5 	ext{ m}$.

Similar Questions

$A$ ball is projected upwards from the top of a tower with a velocity of $50 \, ms^{-1}$ making an angle of $30^{\circ}$ with the horizontal. The height of the tower is $70 \, m$. After how many seconds from the instant of throwing will the ball reach the ground?

$A$ missile is fired in the horizontal direction from a height of $20\,m$ at a speed of $1000\,m/s$. At what horizontal distance from the base will the missile land?

An aeroplane moving horizontally with a speed of $720 \, km/h$ drops a food packet while flying at a height of $396.9 \, m$. The time taken by the food packet to reach the ground and its horizontal range are (Take $g = 9.8 \, m/s^2$):

$A$ particle is dropped from a height of $20\,m$ above horizontal ground. Due to wind,the particle experiences a constant horizontal acceleration of $6\,m/s^2$. Find the horizontal displacement of the particle when it reaches the ground.

$A$ body is projected horizontally from a height with a speed of $20 \, m/s$. What will be its speed after $5 \, s$ (in $, m/s$)? (Take $g = 10 \, m/s^2$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module