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Motion in a Plane — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Plane4 Marks
Question
Read the passage given below and answer the following questions from $i$ to $v.$ we consider the motion of a projectile. An object that is in flight after being thrown or projected is called a projectile. Such a projectile might be a football, a cricket ball, a baseball or any other object. The motion of a projectile may be thought of as the result of two separate, simultaneously occurring components of motions. One component is along a horizontal direction without any acceleration and the other along the vertical direction with constant acceleration due to the force of gravity. It was Galileo who first stated this independency of the horizontal and the vertical components of projectile motion in his Dialogue on the great world systems. Horizontal range of a projectile: The horizontal distance travelled by a projectile from its initial position $(x = y = 0)$ to the position where it passes $y = 0$ during its fall is called the horizontal range, $R$. It is the distance travelled during the time of flight $T_f .$ Therefore, the range $\text{R is R} =(\text{v}_o\cos\theta_o(\text{T}_\text{f})$
$\text{R}=\frac{(\text{v}_\text{o}\cos\theta_\text{o})(2\text{v}_\text{o}\sin\theta_\text{o})}{\text{g}}$
$\text{R}=\frac{(\text{v}_\text{o}^{2}\sin\theta_\text{o})}{g}$ This shows that for a given projection velocity, $R$ is maximum when $2\theta_\text{o}$ is maximum, i.e., when $\theta_\text{o}=45^\circ.$ The maximum horizontal range is, therefore $\text{R}=\frac{\text{v}_\text{o}^2}{g}$ Maximum height of a projectile: Maximum height that can be achieved during projectile and it is given by: $\text{H}_\text{m}=\frac{\text{(v}_\text{o}\sin\theta)^2}{2g}$
  1. Range in projectile motion is maximum when $\theta^\circ:$
  1. $45^0$
  2. $0^0$
  3. $90^0$
  4. None of these
  1. Who was first stated this independency of the horizontal and the vertical components of projectile motion in his Dialogue on the great world system?
  1. Galileo
  2. Newton
  3. Einstein
  4. None of these
  1. What is projectile motion?
  1. What is horizontal range of projectile? Give its formula:
  1. What is maximum height of projectile? Give its formula:
✓

Answer

  1. (a) $45^0$
  2. (a) Galileo
  3. The motion of object under only gravity force in the air is called projectile motion.
  4. The horizontal distance travelled by a projectile from its initial position to the position where it passes same horizontal position during its fall is called the horizontal range, $R$. It is the distance travelled during the time of flight $T_f $. Therefore, the range $R$ is.
$\text{R is R} =(\text{v}_o\cos\theta_o(\text{T}_\text{f})$
$\text{R}=\frac{(\text{v}_\text{o}\cos\theta_\text{o})(2\text{v}_\text{o}\sin\theta_\text{o})}{\text{g}}$
$\text{R}=\frac{(\text{v}_\text{o}^{2}\sin\theta_\text{o})}{g}$
  1. Maximum height of a projectile: Maximum height that can be achieved during projectile and it is given by
$\text{H}_\text{m}=\frac{\text{(v}_\text{o}\sin\theta)^2}{2g}$

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