Prove the well-known result that, for a given launch speed vo, the launch angle = 45° yields the maximum horizontal range R. Determine the maximum range if vo = 25 m/s. (Note that this result does not hold when aerodynamic drag is included in the analysis.) Answer: R = i m
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- The horizontal range of a projectile fired into the air at angle degrees is given by the formula: 2xvxsin 0xcos R 9 m Create a worksheet that computes R for a selected initial velocity vo and angle 0. Use g = 9.81; 15, initial velocity vo 15°, 20°, 25°, ..., 90°. - m S 150 and 0 = 1. Use MAX() function to find the maximum value of R and show that value separately. 2. Create a graph of R versus in degrees.If the ramp is now tilted upward so that “takeoff angle” is now 7.0 degrees above the horizontal, what is the new minimum speed?looking for A and B
- Q.2 A placekicker is attempting to make a 58 m field gonl. If the launch angle of the footbnl) is 40°, what is the minimum initinl speed V wvhich will allow the kicker to succeed? 3 m 0 40° 58 m Not to EcaloA 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…Engineering dynamics. Don't use Artificial intelligence tools.
- This problem will involve deriving a formula or two for a projectile launched from one height and angle and landing at a different height on Earth. Begin with a projectile launched at angle 0 above horizontal from a height y₁ with initial velocity Vo. The projectile lands at a point with height y₂. These are the given quantities: vo, 0, y₁, y2 and g. Construct formulae for each of the following, as. a function of given quantities the horizontal distance traveled. the maximum height reached. the time taken. the angle of impact. (find the final velocity components first).Could I have help with this physics question?Show that the girl at A can throw the ball to the boy at B by launching it at equal angles measured up or down from a 45° inclination. If va = 10 m/s, determine the range R if this value is 15°, i.e., 01 = 45° – 15° = 30° and 02 = 45° + 15° = 60°. Assume the ball is caught at the %3D same elevation from which it is thrown. VA = 10 m/s A В -R-