A small object is thrown at an angle 45^{circ | vedclass

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

Question

(D) Let the object be at point $B(x, y)$ after time $t = \sqrt{2} \,s$. The horizontal displacement is $x = u_x 	imes t = (v_0 \cos 45^{\circ}) 	ime

Vedclass · Accepted Answer

$5 \,m/s$

Vedclass · Answer

(D) Let the object be at point $B(x, y)$ after time $t = \sqrt{2} \,s$. The horizontal displacement is $x = u_x 	imes t = (v_0 \cos 45^{\circ}) 	imes \sqrt{2} = v_0 	imes \frac{1}{\sqrt{2}} 	imes \sqrt{2} = v_0$. The vertical displacement is $y = u_y t - \frac{1}{2} g t^2 = (v_0 \sin 45^{\circ}) \sqrt{2} - \frac{1}{2} (10) (\sqrt{2})^2 = v_0 - 10$. The displacement vector $\vec{OB}$ has magnitude $OB = \sqrt{x^2 + y^2} = \sqrt{v_0^2 + (v_0 - 10)^2}$. The average velocity magnitude is given by $v_{	ext{avg}} = \frac{OB}{t} = |v_0|$. Thus,$OB = |v_0| t = v_0 \sqrt{2}$. Squaring both sides: $v_0^2 + (v_0 - 10)^2 = (v_0 \sqrt{2})^2$. $v_0^2 + v_0^2 - 20v_0 + 100 = 2v_0^2$. $2v_0^2 - 20v_0 + 100 = 2v_0^2$. $20v_0 = 100$,which gives $v_0 = 5 \,m/s$.

Similar Questions

The range of a projectile for a given initial velocity is maximum when the angle of projection is $45^\circ$. The range will be minimum,if the angle of projection is ......... $^\circ$.

$A$ ball is thrown at different angles with the same speed $u$ and from the same point. It has the same range in both cases. If $y_1$ and $y_2$ are the heights attained in the two cases,then $y_1 + y_2$ is equal to:

$A$ body is projected with a velocity $(\hat{i} + 2\hat{j}) \text{ ms}^{-1}$,where $\hat{i}$ is along the horizontal and $\hat{j}$ is vertically upward. Then the equation of its trajectory is $(g = 10 \text{ ms}^{-2})$.

$A$ projectile is fired at an angle of $45^{\circ}$ with the horizontal. The elevation angle of the projectile at its highest point as seen from the point of projection is:

$A$ bullet is dropped from a certain height,and at the same instant,another bullet is fired horizontally from the same height. Which bullet will hit the ground first?

Vedclass Test Series

Exam Paper Generator

Online Exam Module