Question
Prove that the path of a projectile is a parabola.
✓
Answer
Consider a projectile thrown at an angle $\theta$ with a velocity u. The components of velocity horizontal and vertical are $\text{u}\cos\theta$ and $\text{u}\sin\theta.$ After time t, the horizontal displacement $\text{x}=\text{u}\cos\theta\text{t}$
The vertical displacement, $\text{y}=\text{u}\sin\theta\text{ t}-\frac{1}{2}\text{gt}^2$ $\therefore\ \text{y}=\text{u}\sin\theta.\Big(\frac{\text{x}}{\text{u}\cos\theta}\Big)-\frac{1}{2}\text{g}\Big(\frac{\text{x}}{\text{u}\cos\theta}\Big)^2$ $\text{y}\propto\text{x}^2,$ the path of a projectile is a parabola.
The vertical displacement, $\text{y}=\text{u}\sin\theta\text{ t}-\frac{1}{2}\text{gt}^2$ $\therefore\ \text{y}=\text{u}\sin\theta.\Big(\frac{\text{x}}{\text{u}\cos\theta}\Big)-\frac{1}{2}\text{g}\Big(\frac{\text{x}}{\text{u}\cos\theta}\Big)^2$ $\text{y}\propto\text{x}^2,$ the path of a projectile is a parabola.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A body of mass 15 kg is hung by a spring balance in a lift. What would be the reading of the balance when
i. the lift is ascending with an acceleration of $2 ms^{-2}$
ii. descending with the same acceleration
iii. descending with a constant velocity of $2 ms^{-1}$ ?
Take $g =10 ms^{-2}$.
→i. the lift is ascending with an acceleration of $2 ms^{-2}$
ii. descending with the same acceleration
iii. descending with a constant velocity of $2 ms^{-1}$ ?
Take $g =10 ms^{-2}$.
Establish a relation between angular momentum and moment of inertia of a rigid body. Define moment of inertia in terms of it.
What is the true weight of an object in a geostationary satellite that weighed exactly 10.0N at the north pole?
Show that range of projection of a projectile for two angles of a projection $\alpha$ and $\beta$ is same where $\alpha+\beta=90^\circ.$
→Estimate the average mass density of a sodium atom assuming its size to be about $2.5 \mathring{\text{A}}.$ (Use the known values of Avogadro’s number and the atomic mass of sodium). Compare it with the mass density of sodium in its crystalline phase: $970kg m^{–3}. $Are the two densities of the same order of magnitude? If so, why?
→The velocities of ten particles in $ms^{-1}$ are $0, 2, 3, 4, 4, 4, 5, 5, 6, 9.$ Calculate $(i)$ Average speed and $(ii) \text{r.m.s}.$ speed.
→A thin prism of crown glass $(\mu_\text{r}=1.515,\mu_\text{v}=1.525)$ and a thin prism of flint glass $(\mu_\text{r}=1.612,\mu_\text{v}=1.632)$ are placed in contact with each other. Their refracting angles are 5.0° each and are similarly directed. Calculate the angular dispersion produced by the combination.
→Two vessels have the same base area but different shapes. The first vessel takes twice the volume of water that the second vessel requires to fill upto a particular common height. Is the force exerted by the water on the base of the vessel the same in the two cases ? If so, why do the vessels filled with water to that same height give different readings on a weighing scale?
The photograph of a house occupies an area of $1.75cm^2$ on a $35mm$ slide. The slide is projected on to a screen, and the area of the house on the screen is $1.55m^2$. What is the linear magnification of the projector-screen arrangement.
→Two stars each of one solar mass ($= 2 \times 10^{30}kg$) are approaching each other for a head on collision. When they are a distance $10^9km$, their speeds are negligible. What is the speed with which they collide? The radius of each star is $10^4km.$ Assume the stars to remain undistorted until they collide. (Use the known value of G).
→