Question:
A projectile is launched from the ground, such that it hits a target on the ground which is \(90\,\text{m}\) away. The minimum velocity of projectile to hit the target is \((\text{acceleration due to gravity}=10\,\text{m s}^{-2})\)
A projectile is launched from the ground, such that it hits a target on the ground which is \(90\,\text{m}\) away. The minimum velocity of projectile to hit the target is \((\text{acceleration due to gravity}=10\,\text{m s}^{-2})\)
Show Hint
For maximum range with minimum speed on level ground, use
\[
R_{\max}=\frac{u^2}{g}
\]
which occurs when \(\theta=45^\circ\).
Updated On: Jun 22, 2026
- \(10\,\text{m s}^{-1}\)
- \(16\,\text{m s}^{-1}\)
- \(60\,\text{m s}^{-1}\)
- \(30\,\text{m s}^{-1}\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Use the range formula for projectile motion.
For a projectile launched and landing at the same level, the horizontal range is \[ R=\frac{u^2\sin 2\theta}{g} \] Here, \[ R=90\,\text{m} \] and \[ g=10\,\text{m s}^{-2} \]
Step 2: Find condition for minimum velocity.
For a given range \(R\), the velocity \(u\) will be minimum when \(\sin 2\theta\) is maximum.
The maximum value of \[ \sin 2\theta \] is \[ 1 \] So, \[ R=\frac{u^2}{g} \]
Step 3: Substitute the given values.
\[ 90=\frac{u^2}{10} \] \[ u^2=900 \] \[ u=30\,\text{m s}^{-1} \]
Step 4: Final conclusion.
Therefore, the minimum velocity of the projectile is \[ \boxed{30\,\text{m s}^{-1}} \]
For a projectile launched and landing at the same level, the horizontal range is \[ R=\frac{u^2\sin 2\theta}{g} \] Here, \[ R=90\,\text{m} \] and \[ g=10\,\text{m s}^{-2} \]
Step 2: Find condition for minimum velocity.
For a given range \(R\), the velocity \(u\) will be minimum when \(\sin 2\theta\) is maximum.
The maximum value of \[ \sin 2\theta \] is \[ 1 \] So, \[ R=\frac{u^2}{g} \]
Step 3: Substitute the given values.
\[ 90=\frac{u^2}{10} \] \[ u^2=900 \] \[ u=30\,\text{m s}^{-1} \]
Step 4: Final conclusion.
Therefore, the minimum velocity of the projectile is \[ \boxed{30\,\text{m s}^{-1}} \]
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET Projectile motion Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A body is projected vertically upwards with a velocity u. It crosses a point in its journey at a height h twice, just after 1 and 7 s. The value of $ \mu $ is ms-1 is: $ (g=10{{m}^{-2}}) $
- A body is projected horizontally from the top of a tower of height $180\, m$ with a velocity of $20 \, ms^{-1}$. If acceleration due to gravity is $10 \, ms^{-2}$ then match the following.
List-I List-II A Velocity of the body after 1 second (in $ms^{-1}$) I 5 B Horizontal displacement of the body after 1 second (in meters) II 20 C Vertical displacement of the body after 1 second (in meters) III 10 D Vertical velocity of the body after 1 second (in $ms^{-1}$) IV 22.4 - Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion (A): The velocity of a projectile at a point on its trajectory is equal to the slope at that point.
Reason (R): The velocity vector at a point is always along the tangent to the trajectory at that point.
In the light of the above statements, choose the correct answer from the options given below - A particle is projected up from a point at an angle 9, with the horizontal direction. At any time t, if p is the linear momentum, y is the vertical displacement, x is the horizontal displacement, the graph among the following, which does not represent the variation of kinetic energy K of the projectile is
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions