Question

Suppose a baseball player throws a ball. When she releases the ball, her hand is 1 meter above the ground, and the ball leaves her hand at 18 m/s in a direction that makes a 32° angle with the horizontal. (a) What is the maximum height above the ground that the ball reaches? (b) For how much total time is the ball in the air before it hits the ground? (Be careful!) (c) How far from the player does the ball hit the ground? 7. In OpenStax Section 3.4, an equation that is sometimes known as the "range equation" is given without proof: (1) R=" sin(20), 9 where vo is the initial velocity, 0 is the angle the initial velocity makes with the ground, and the range R is the distance a projectile travels over level ground, neglecting air resistance and assuming that the projectile starts at ground level. This equation isn't actually new information, but rather it is just a combination of the kinematics equations we've already seen many times. Your job is to derive and prove this equation by considering a projectile undergoing this sort of motion and using the kinematic equations. Like in Problem 1 of this assignment, we know the outcome; the point here is to go through the exercise of carefully understanding why it is true. (a) Start from the kinematic equation for y(t) = -3gt2 + voyt + yo notice that here we are calling ga positive number and putting the negative sign out in front in the equation instead, because that is what OpenStax did here – it's just a notation choice). Call the ground level y = 0 and set yo appropriately. When the projectile motion is completely finished and the ball has returned to the ground, what is y(t) equal to? Write down the equation for this moment and solve for t. (b) Notice that the range R is really just another name for xf - 20. Use this fact, the kinematic equation for x(t), and your result from part (a) to find an equation for R in terms of vo, 0, and g.

Could I get help with these problems please. For the first problem are we using two different equations. Are we using a horizontal and vertical equation. V(t)=axt+vox. I am confused here

Answer 1