Two particles are projected from the same point with the same speed $$u$$ such that they have the same range $$R$$, but different maximum heights, $$h_1$$ and $$h_2$$. Which of the following is correct?
For same range angle of projection will be $$\theta \& 90 - \theta$$
$$R = \dfrac{u^2 2\sin \theta \cos \theta}{g}$$
$$h_1 = \dfrac{u^2 \sin^2 \theta}{g}$$
$$h_2 = \dfrac{u^2 \sin^2 (90 - \theta)}{g}$$
$$\dfrac{R^2}{h_1h_2} = 16$$
A body is projected at $$t = 0$$ with a velocity $$10 ms^{1}$$ at an angle of $$60$$ with the horizontal.The radius of curvature of its trajectory at $$t = 1s$$ is $$R$$. Neglecting air resistance and taking acceleration due to gravity $$g = 10\,\, ms2$$, the value of $$R$$ is :
A plane is inclined at an angle $$\alpha = 30^o$$ with a respect to the horizontal. A particle is projected with a speed $$u = 2 ms^{-1}$$ from the base of the plane, making an angle $$\theta = 15^o$$ with respect to the plane as shown in the figure.The distance from the base, at which the particle hits the plane is close to : (Take $$g = 10 ms^{-2}$$)
In a soccer practice session the ball is kept at the centre of the field $$40$$ yards from the $$10\ ft$$ high goal post . A goal is attempted by kicking the ball at a speed of $$64\ ft/s$$ at an angle of $$45^0$$ to the horizontal. Will the ball reach the goal post ?
Two projectiles A and B are projected with angle of projection $$15^0$$ for the projectile A and $$45^0$$ for the projectile B. If $$R_A$$ and $$R_B$$ be the horizontal range for the two projectiles, then
The range of a projectile fired at an angle of $$15^{o}$$ is $$50\ m$$. If it is fired with the same speed at an angle of $$45^{o}$$, its range will be
A body projected with velocity u at projection angle $$\theta$$ has horizontal displacement R. For the same velocity and projection angle, its range on the moon surface will be?
Three balls of same masses are projected with equal speeds at angle $$15^o, 45^o, 75^o$$ and their ranges are respectively $$R_1, R_2$$ and $$R_3$$ then:
A projectile can have the same range R for two angles of projection $$\theta$$ and $$(90^o-\theta)$$. If $$t_1$$ and $$t_2$$ are the times of flight in the two cases then:
Two stones are projected with same velocity v at an angle $$\theta$$ and $$(90^o-\theta)$$. If H and $$H_1$$ are greatest heights in the two paths, what is the relation between R, H and $$H_1$$?
The range of projectile projected at an angle $$15^o$$ is $$10\sqrt{3}$$m. If it is fired with the same speed at angle of $$30^o$$, its range will be?