A fireworks rocket explodes at height h, the peak of its vertical trajectory. It throws out burning fragments in all directions, but all at the same speed v. Pellets of solidified metal fall to the ground without air resistance. Find the smallest angle that the final velocity of an impacting fragment makes with the horizontal.

SITUATION 9. A small projectile is fired vertically downward into a fluid medium with an initial velocity of 60m/s. Due to the drag resistance of the fluid the projectile experiences a deceleration of a = -0.4v³m/s², where v is in m/s. Determine the projectile's velocity and position 4 s after it is fired.

Calculate the magnitude

A golfer gives a ball a maximum initial speed of 51.8 m/s. What is the longest possible hole-in-one for this golfer? Neglect any distance the ball might roll on the green and assume that the tee and the green are at the same level. What is the minimum speed of the ball during this hole-in-one shot?

Danielle launches a ball off of a platform of height h with velocity vo at an angle 0 above the horizontal. A wall with a ball-sized hole a height H above the floor, with H > h, is a horizontal distance L = 24.0 m away from Danielle. The difference in height between H and h is one-twelfth of L, and the square of the magnitude of the velocity, v, is three-halves of the product gL. H 1 H – h = h 3 L Determine the two values of 0 that ensure the ball passes through the hole. Submit the larger angle as 0, and the smaller angle as 02.

The banded archerfish is a species of fish that lives in mangrove estuaries in Asia and Oceania. It has a unique and highly effective hunting strategy: it shoots an incredibly precise stream of water out of its mouth at almost ten meters per second, knocking insects and other small animals into the water from nearby branches! Pom Fbug (t) Ө = Our hero, a hungry archerfish, has spotted a big, delicious bug sitting on a branch a height ħ above the surface of the water. The archerfish can shoot its water jet at a speed of vo. The archerfish wants to knock the bug sideways off of the branch, so it decides to shoot so that its water jet is moving horizontally at the moment when it strikes the bug. The final goal of this problem is to find the horizontal distance, d, from the branch, and the angle above horizontal, 0, at which archerfish should shoot. d (a) What are the position and velocity of the water droplet as a function of time and the position and velocity of the bug as a function of…

As part of an obstacle course, an athlete must kick a soccer ball into a 1 meter wide and 10 meter deep pit such that the ball hits a target at the bottom of the pit. In practice, a dynamics student that is participating in the race kicks the soccer ball such that the soccer ball will bounce off the far wall of the pit 5 meters below the surface and head towards the target. If the velocity of the ball before striking the wall at point at point A is v4 = 2.6i – 10j m, determine the t-component of the ) after striking the wall. The size of the ball and the target ball velocity vector (in are negligible relative to the dimensions of the pit, the gravity acceleration must be considered as g 10 m and the coefficient of restitution at point A is e =0.35. 5 m t 10 m 1m 三

We want to find the coefficient of restitution e between the ball and the floor. We will be able to measure the time of flight between subsequent bounces, but not the velocities before and after each impact. Question 1 a. Using the kinematics equation for position, find a relationship between the time of flight tn and the velocity of the ball after the nth bounce. You should obtain a quadratic equation that has two solutions for the time tm, but only one of them represents the time of flight. b. Using the kinematics equation for velocity and the relationship determined in the previous step, find the relationship between the velocity right after the nth bounce and the velocity right before the (n +1)th bounce? c. Given your answers to the previous parts of this question and the definition of €, find the coefficient of restitution e in terms of the subsequent times of flight tn and tr+1.

Hole number 7 at Pebble Beach golf course is one of the shortest championship holes in the world. The hole is only 100m away from the tee, and it is also 12m lower. Champion golfer Shooter McGavin hits a 9-iron at an angle of 50◦ with respect to the horizontal, and lands the ball right in the hole. Assume there is no wind or air resistance, and g = 9.8 m/s^2. (sin 50◦ = 0.766, cos 50◦ = 0.643, tan 50◦ = 1.19, sin 45◦ = 0.707, cos 45◦ = 0.707, tan 45◦ = 1.00). What is the initial velocity of the ball? How long was the ball in the air? What was the maximum height? If Shooter had misjudged the hole, and hit the ball with the same velocity but at an angle of 45◦ instead, by how much would he have overshot the hole?

You are investigating an accident that occurred early on a foggy morning in Oxfordshire. A 2015 Prius Hatchback traveling due north collided in a highway intersection with a 2012 Nissan Pathfinder that was traveling due east. After the collision, the wreckage of the two vehicles was locked together and skidded across the level ground until it struck a tree. You measure that the tree is 11 m from the point of impact. The line from the point of impact to the tree is in a direction 39° north of east. From experience, you estimate that the coefficient of kinetic friction between the ground and the wreckage is 0.45. Shortly before the collision, a police officer with a laser speed gun measured the speed of the Prius to be 80 km/h and, according to a witness, the Prius driver made no attempt to slow down. Four people with a total mass of 230 kg were in the Nissan. The only person in the Prius was the 80 kg driver. The Nissan with its passengers had a mass of 2362 kg, and the Prius with its…