Derive the formula for the horizontal range, R of a projectile having an initial speed Vo and an angle of projection Ɵo. Then show that the projection angle of 45o gives the maximum horizontal range.

Q: An object is projected straight upwards with an initial velocity U. If T is the time taken to return…

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Q: A mortar gu, with a maximum range of 20 m on level ground, is placed on the edge of a vertical cliff…

A: As the request is for (b), I will answer only (b)   Given, Range (R) = 20m. The mortar gun is placed…

Q: For a projectile lunched with an initial velocity of vo at an angle of e (between 0 and 90°), a)…

A: The components of v0 are expressed as follows: vinitial-x=v0cosθvinitial-y=v0sinθ (a) Let us first…

Q: A projectile is fired with an initial velocity of 244 mps at a target B located 610 m above the gun…

A: Given that,  A projectile is fired with u=244m/s  target 'B' located at 610m above the gun A,  at…

Q: An arrow at angle of 25° is moving at a rate of 15 m/s, find the final velocity (along the X and Y…

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Q: A projectile projected with the initial velocity 25 m/s with the lunching angle of 30°. Find the…

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Q: Keeping the angle of projectile constant, the velocity of projection is double. What is the effect…

A: The equation for the horizontal range is given by

Q: The speed of a projectile in the horizontal direction is constant. O True O False

A: For a projectile the only force acting on it is gravitational force and it is acting downward in…

Q: A projectile is launched with an initial velocity of 100 m/s at a 30° angle above the horizontal.…

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Q: Find the position vector of a particle whose acceleration vector is a=(6t,2) with an initial…

A: Write the expression for the acceleration, and solve for the velocity vector.

Q: Prove the well-known result that, for a given launch speed vo, the launch angle 0 = 45° yields the…

A: To prove that for a given launch speed v0, the launch angle θ = 45o yields the maximum horizontal…

Q: In the figure, a ball is thrown leftward from the left edge of the roof, at height h above the…

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Q: A projectile is launched with a launch angle of 50° with respect to the horizontal direction and wit

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Q: At what angle should a projectile be launched to attain maximum range? O 45 degrees O 25 degrees O o…

A: There are various factors that can affect the maximum projectile range of a projectile. It includes…

Q: In the figure, a ball is thrown leftward from the left edge of the roof, at height h above the…

A: c. the initial velocity can be calculated as

Q: A cannon ball is fired from point A with a horizontal muzzle velocity of 120 m/s. Ifthe cannon is…

A: Given data: The initial horizontal velocity of the ball, ux=120 m/s. The height from which the ball…

Q: Consider a projectile fired with an initial velocity perpendicular to an incline sloping downward at…

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Q: For a projectile lunched with an initial velocity of vo at an angle of 8 (between O and 90°), a)…

A: We know that the projectile reaches the high point of its trajectory (vy = 0) so that at time…

Q: A projectile is fired with initial velocity of 350 m/sec., and with an angle of 50 degree with…

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Q: The speed of a projectile when it reaches its maximum height is 0.35 times its speed when it is at…

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Q: For a projectile lunched with an initial velocity of vo at an angle of e (between 0 and 90°), a)…

A: (a) The components of the initial velocity along x and y direction can be written as v0x=v0cosθ…

Q: Suppose a projectile is launched at an angle of 60° above the horizontal. If the initia speed of the…

A: Given  Angle =60°  Projectile speed=v= 200 ft/ sec  Acceleration due to gravity =32 ft/sec²  Let x,y…

Q: Why an angle of 45 degrees gives the largest range possible in case of projectile motion

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Q: The magnitude of the velocity of a projectile remains constant. Is it correct?

A: For a projectile, the horizontal velocity always remains constant due to absence of any acceleration…

Q: A projectile can have the same range R' for two angles of projection. If 'T,' and 'T,' to be time of…

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Q: The speed of a projectile when it reaches its maximum height is one-half its speed when it is at…

A: let the initial velocity = u Let the launch angle = θ

Q: A particle is projected from the ground with an initial speed of '' at angle 0 with horizontal. The…

A: The maximum height reached At this moment the particle would have crossed a distance equal to half…

Q: What relation exists between the range covered by two projectiles thrown up with the same initial…

A: The range of a projectile is given by R=u2 sin 2θg                             (1) where u=initial…

Q: Find the angle of projection at which the maximum height reached by a projectile is twice the…

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Q: The projectile at A is projected with an initial velocity v=23 m/s and an angle of projection theta…

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Q: A position vector with magnitude 10 m points to the right and up. Its x-component is 6.0 m. What is…

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Q: A target lies a distance R = 1100 m from a cannon across level ground, and a distance d = 780 m…

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Q: A projectile is fired vertically from point A with an initial speed of 250 ft/sec. Relative to an…

A: Given u =250 ft/s AB=375'=37512=31.25 ftθ=32°

Q: If a particle's position is described by r(t) = e*i+te“j, find the velocity and acceleration vectors…

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Q: A projectile is fired at an angle a to the vertical. ts horizontal range will be maximum when a is

A: Expression for Range=u2sin2αg for initial velocity u, the range is maximum when sin gives maximum…

Q: A projectile is launched with an initial speed of 200m/s at an angle of 60° with respect to the…

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Q: A projectile is launched with a velocity of 25 m/s at an angle of 20 degrees with respect to the…

A: Given: The velocity is v=25 m/s. The angle is θ=20°. The expression for initial velocity along the…

Q: In archery, should the arrow be aimed directly at the target?How should your angle of aim depend on…

A: As the effect of gravity fall over the arrow, the arrow may move downward direction.

Q: A bullet is fired at an angle of 60° to the horizontal with an inital velocity of 200m/s. How long…

A: Initial velocity of bullet = 200 m/s Angle made with horizontal = 60° Time of flight of bullet…

Q: Compute for the initial velocity of a projectile launched at 30 degrees with a range of 25m. If the…

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Q: An arrow is shot upward from the ground, with an initial velocity of 86 meters per second, at an…

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Q: What is the maximum height reached by a projectile where y=15t-5t3?

A: for a projectile : y = 15t - 5t3To find : The maximum height reached by the projectile

Projectile Motion