A projectile is fired in such a way that its horizontal range is equal to 9.5...

Question

Question

A projectile is fired in such a way that its horizontal range is equal to 9.5 times its maximum height. What is the angle of projection?

Answer 1

Answer #1

Horizontal Range = v² sin2θ/g

Height = v² sin²θ/2g

According to the question

v² sin2θ/g= 9.5 x v² sin²θ/2g

=>2v² sinθcosθ/g= 9.5 x v² sin²θ/2g

=> 4/9.5=sinθ/cosθ [On Simpplification]

=>tanθ=4/9.5=> θ==22.83⁰

Hence the angle of Projection is 22.83⁰ with respect to the horizontal.

Answer 2

Similar Homework Help Questions

a projectile is fired in such a way that its horizontal range is equal to three times its...

a projectile is fired in such a way that its horizontal range is equal to three times its maximum hight. what is the angle of projection?
A projectile is fired with an initial speed of 10 m/s. Find theangle of projection...

A projectile is fired with an initial speed of 10 m/s. Find the angle of projection such that the maximum height of the projectile is equal to 0.9 times its horizontal range.
please show worked problem; The range R of a projectile fired from the origin over horizontal...

please show worked problem; The range R of a projectile fired from the origin over horizontal ground is the distance from the origin to the point of impact. If the projectile is fired with an initial velocity v0 at an angle a with the horizontal, then the range is given by the formula below, where g is the downward acceleration due to gravity. Find the angle a for which the range R is the largest possible. R = v^2/g sin...

A projectile fired from a gun has initial horizontal and vertical components of velocity equal to...

A projectile fired from a gun has initial horizontal and vertical components of velocity equal to 30 m/s and 40 m/s, respectively. a. determine the initial speed of the projectile b. at what angle is the projectile fired (measured with respect to the horizontal)? c. approximately how long does it take the projectile to reach the highest point in its trajectory?
A projectile is fired from the ground (you can assume the initial height is the same...

A projectile is fired from the ground (you can assume the initial height is the same as the ground) in a field so there are no obstacles in its way. It is fired at an angle of 24° with respect to the horizontal and with an initial speed of 25 m/s. Air resistance is negligible in this situation. Call up the positive y-direction, and toward the wall the positive x-direction. What is the earliest time when the height of the...
A projectile is fired from the ground (you can assume the initial height is the same...

A projectile is fired from the ground (you can assume the initial height is the same as the ground) in a field so there are no obstacles in its way. It is fired at an angle 11° with respect to the horizontal and with an initial speed of 46 m/s. Air resistance is negligible in this situation. Call up the positive y direction, and toward the wall the positive x direction. What is the earliest time when the height of...

Extra Credit (+3% maximum): The range R of a projectile fired with an initial velocity vo...

Extra Credit (+3% maximum): The range R of a projectile fired with an initial velocity vo at an angle with the horizontal is given by R = ama where g is the acceleration due to gravity. Find the acute angle such that the range is a maximum.
A 60.0-kg projectile is fired at an angle of 30.0° above the horizontal with an initial...

A 60.0-kg projectile is fired at an angle of 30.0° above the horizontal with an initial speed of 124 m/s from the top of a cliff 144 m above level ground, where the ground is taken to be y = 0. (a) What is the initial total mechanical energy of the projectile? (Give your answer to at least three significant figures.) (b) Suppose the projectile is traveling 87.9 m/s at its maximum height of y = 304 m. How much...
A projectile is fired with an initial speed of 20. m/s at an angle of 42.2°...

A projectile is fired with an initial speed of 20. m/s at an angle of 42.2° above the horizontal on a long flat firing range. Determine, a) the maximum height reached by the projectile, b) the total time in the air, c) the total horizontal distance covered (that is, the range), d) the speed of the projectile 1.50 s after firing. e) direction of the speed at 1.50 s.

A 44.0-kg projectile is fired at an angle of 30.0° above the horizontal with an initial...

A 44.0-kg projectile is fired at an angle of 30.0° above the horizontal with an initial speed of 128 m/s from the top of a cliff 160 m above level ground, where the ground is taken to be y = 0. (a) What is the initial total mechanical energy of the projectile? (Give your answer to at least three significant figures.) ____J (b) Suppose the projectile is traveling 90.7 m/s at its maximum height of y = 331 m. How...