Discuss separately, how the angle of projection varies with Time, Range and Height  for a fixed speed of a projectile. Discuss separately, how the velocity of projection varies with Time, Range and Height for a fixed angle of a projectile.

A projectile is fired with initial speed 150 m/s and an angle of elevation 45° from a position 10 m above ground level. Where does the projectile hit the ground and with what speed? Solution If we place the origin at ground level, then the initial position of the projectile is  (0, 10)  and so we need to adjust the parametric equations of the trajectory by adding 10 to the expression for y. With  v0 = 150 m/s,  ? = 45°, and g = 9.8 m/s2, we have x  =  150 cos    ? 4    t =          y  =  10 + 150 sin    ? 4    t −  1 2  (9.8)t2 =          . Impact occurs when y = 0, that is  4.9t2 − 75   2  t − 10 = 0.  Solving this quadratic equation (and using only the positive value of t), we get the following. (Round your answer to two decimal places.) t =  75   2  +    11,250 + 196 9.8  ≈   Then  x ≈ 75   2 (21.74) ≈    (rounded to the nearest whole number), so the projectile hits the ground about…

Lesson: Projectiles If two projectiles have the same size and shape but one is heavier than the other, which will travel further horizontally if they are both launched at the same angle and speed? O The heavy one O They will both be the same O The light one O Not enough information to tell

Use a graphing utility to obtain the path of a projectile launched from the ground (h = 0) at the specified values of θ = 35°, v0 = 300 feet per second. In the exercise, use the graph to determine the maximum height and the time at which the projectile reaches its maximum height. Also use the graph to determine the range of the projectile and the time it hits the ground. Round all answers to the nearest tenth.

Anthony carelessly rolls his toy car off a 79.0-cm-high table. The car strikes the floor at a horizontal distance of 96.0 cm from the edge of the table. (a) What was the velocity with which the car left the table? (Enter the magnitude.)(b) What was the angle of the car's velocity with respect to the floor just before the impact?

A particle is projected with a velocity such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where g is acceleration due to gravity)

Projectile #1 is launched at t%=DOs at position (0,0) with an initial x-velocity of 5m/s and y-velocity of 10m/s. Projectile #2 is launched 1s after projectile #1 from an initlal position of (1,1) with an x-velocity of 10m/s. Find the following: The position that the 2 projectiles collide at, the time it takes to collide, and the Initial velocity of projectile #2 Including the launch angle.

Question 2. A projectile is fired from the ground with an initial speed v at an angle 0 above the horizontal. (a) At t = 0, what is the velocity vector? (b) At what time t' does the projectile reach its maximum height? (c) What is the velocity vector at the top of the trajectory? (d) What is the horizontal distance traveled by the projectile? (e) At what angle should one launch the projectile to maximize horizontal distance traveled?

Projectile A is launched at an angle of 20 degrees to the horizontal with initial speed u. Projectile B is launched at an angle of 70 degrees to the horizontal, also with an initial speed u.(a) Compare the times of flight of the two projectiles.(b) Show that the ranges of both projectiles are equal.

A river of width' a'with straight parallel banks flows due north with speed u. The points O and A are on opposite banks and A is due east of O. Coordinate axes Ox and Oy are taken in the east and north directions respectively. A boat, whose speed is v relative to water, starts from O and crosses the river. If the boat is steered due east and u varies with x as : u = x(a – x)- Find : absolute velocity of boatman when he reaches the opposite bank