A biathlete skis up to the shooting range knowing that a single bullseye will win her the gold medal. She raises her rifle such that it is at the same height as the bullseye a distance R meters away. If the initial velocity of the bullet leaving her rifle is v0, find an expression for the height above the bullseye she must aim in order to hit the bullseye. Solve your equation with the values R = 100 m and v0 = 300 m/s. Hint: you might find using a trig identity helpful.

After discovering that two hikers have been stranded on Devil’s Thumb Pass, the Colorado Search andRescue team sends out a plane with supplies for the hikers. Because the hikers are in an isolated location, theplane has to drop the supplies as it fies overhead (see Figure 1). If the plane is 235 m above the hikers andhas a horizontal speed of 200 km/h, how far away from the hikers should the supplies be dropped if they areto land at the hikers’ location?

Consider a projectile being launched with an initial speed of 43 m/s at a variety of initial angles. Refer to the figure. What is the range, in meters, of the projectile if it is launched at an angle of θ1 = 79.7°?  What is the range, in meters, of the projectile if it is launched at an angle of θ2 = 40.5°?  What is the range, in meters, of the projectile if it is launched at an angle of θ3 = 90 − 79.7°, the complement of θ1?

Q1-A 2.0 meter tall basketball player is standing on the floor a distance from the basket. He shoots the ball at an angle of 23 degrees above the horizontal with a speed of 9.6 m/s and makes the shot. If the ball goes in the hoop at 5 seconds, what is the height of the hoop?

A catfish is spotted at the bottom of a creek. The depth of the water is 2 m. A hunter (with no knowledge ofoptics) fires a rifle shot, directly aimed at the catfish. The bullet strikes the water at an angle of 40° to the water. Assumethat the bullet is not deflected by the air/water interface, what is the distance from the bullet hole at the bottom of the creekto the catfish?A) 0.88 mB) 0.97 mC) 0.49 mD) 0.56 mE) 0.73 m

A projectile is shot on level ground with ahorizontal velocity of 17 m/s and a verticalvelocity of 39 m/s. Find the time the projectile is in the air.The acceleration due to gravity is 9.8 m/s. Answer in units of s. Find the range R.Answer in units of m. Let the magnitude of v0 be the same as in part1, but consider the angle θ required to obtainthe maximum range.Find the height attained for the maximumrange.Answer in units of m.

Consider a projectile launched at a height h feet above the ground and at an angle ? with the horizontal. If the initial velocity is v0 feet per second, the path of the projectile is modeled by the parametric equations x = t(v0 cos(?)) and y = h + (v0 sin ?)t - 16t2.Let h=6, v0=63.25, and ?=0.79.  What is the range of the projectile (i.e., how far does it travel? Round your answers to two decimal places).

In my homework, I am asked to derive an equation for V0.   The homework question is as follows: A howitzer fires a shell with a velocity of v0 at an angle Θ above the horizontal. The howitzer is on a plateau and the shell lands down in the plain below, a vertical distance d below the plateau and a horizontal distance L from where the howitzer is. Derive an expression for the magnitude of the initial velocity, V0, as a function of d, L, g, and Θ.   Any help would be appreciated as I have worked on this problem for quite a while and I am not making progress.

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.

You are designing a missile defense system that will shoot down incoming missiles that pass over a perimeter defense post. The set-up is shown below. An incoming missile passes directly above the defense base. Radar at the base can measure the height, h, and speed, v1, of the incoming missile. Your Patriot Rocket is set to fire at an angle of θ=67∘ from vertical. You design the Patriot Rocket so the magnitude of its acceleration is given by: a2=Ae^−bt where A can be set on your Patriot Rocket as it is fired, b=0.15 s−1, and t=0 s when it is fired. The direction of your Patriot Rocket's vector acceleration stays at the same angle, θ, for the entire trip. If an incoming missile passes over the defense base at a height of 4.7 km and at a constant speed of 757 m/s (this means that v→1 is constant), solve for the value of A your Patriot Rocket must have in order to hit the incoming missile. You will also need to enter results from intermediate steps of your calculation, including the…