# Motion in a Plane

## Several particles are thrown from a point in various directions but with the same initial speed vₒ. At any subsequent time t before they reach the ground, they lie on the surface of

Q: Several particles are thrown from a point in various directions but with the same initial speed vₒ. At any subsequent time t before they reach the ground, they lie on the surface of

(a) parabolic

(b) sphere

(c) ellipsoid

(d) straight line

Ans: (b)

## A gun can fire shells with maximum speed and the maximum horizontal range that can be achieved is R = vo^2/g . If a target farther away by distance Δx (beyond R ) has to be hit with the same gun, show that it could be achieved by raising the gun to a height at least h = Δx [1+ Δx/R]

Q: A gun can fire shells with maximum speed and the maximum horizontal range that can be achieved is R = vo^2/g . If a target farther away by distance Δx (beyond R ) has to be hit with the same gun, show that it could be achieved by raising the gun to a height at least h = Δx [1 + Δx/R]

## A stone is to be projected horizontally from top of a 1.7 m high pole. Calculate initial velocity of projection (in ms-1), if strikes perpendicularly an inclined plans as shown in the figure.

Q: A stone is to be projected horizontally from top of a 1.7 m high pole. Calculate initial velocity of projection (in ms-1), if strikes perpendicularly an inclined plans as shown in the figure.

Ans: 3

## A fountain consist of a small hemispherical sprayer which lies on the surface of water in a basin as shown in the figure. The sprayer has in numerable small holes through which water spurts at same speed 10 ms-1 in all directions. Choose the correct option(s)

Q: A fountain consist of a small hemispherical sprayer which lies on the surface of water in a basin as shown in the figure. The sprayer has in numerable small holes through which water spurts at same speed 10 ms-1 in all directions. Choose the correct option(s)

(a) The shape of water bell formed by the jets is parabolic

(b) The maximum height attained by the water is 5 m

(c) The diameter of the basin be at least 20 m If no water is to be lost

(d)  None of the above

Ans: (a) , (b) , (c)

## Two stones A and B are thrown simultaneously from a point on horizontal ground. The stone A is thrown vertically up with velocity uA and the stone B is thrown with speed uB at angle 37° with horizontal . After 0.9 sec stones are moving perpendicular to each other. Then,

Q: Two stones A and B are thrown simultaneously from a point on horizontal ground. The stone A is thrown vertically up with velocity uA and the stone B is thrown with speed uB at angle 37° with horizontal . After 0.9 sec stones are moving perpendicular to each other. Then,

(a) uA > 9ms-1

(b) uB > 9ms-1

(c) uB= 15ms-1

(d) uB= 9ms-1