Question

The gravitational force on a baseball is -Fgĵ. A pitcher throws the baseball with velocity vî by uniformly accelerating it straight forward horizontally for a time interval Δt = t − 0 = t. If the ball starts from rest, determine the following: (Use any variable or symbol stated above along with the following as necessary: g for the acceleration due to gravity.)

(a) Through what distance does it accelerate before its release?
d =
(b) What force does the pitcher exert on the ball?
P =

Second Question:

Two forces, 1 = (2.95î + 2.60ĵ) N and 2 = (4.75î + 8.85ĵ) N, act on a particle of mass 2.40 kg that is initially at rest at coordinates (−2.15 m, +3.95 m).

(a) What are the components of the particle's velocity at t = 11.2 s?
=..........m/s

(b) In what direction is the particle moving at t = 11.2 s?
............° counterclockwise from the +x-axis

Answer 1

Kinematics and dynamics principles in Physics are used to calculate the distance a baseball accelerates and the force exerted by a pitcher, as well as determining the velocity components and direction of a moving particle under the influence of two forces.

Step-by-step explanation:

The questions presented cover topics from Physics, specifically kinematics and dynamics, which are often studied in high school. The first question involves calculating the distance over which a baseball accelerates before being thrown and the force exerted by the pitcher. As the ball starts from rest and accelerates over a time interval Δt, you can use the equation of motion d = (1/2)at² to find the distance d, where a is the acceleration. To determine the force exerted by the pitcher (P), we apply Newton's second law F = ma, using the final velocity divided by the time interval as the acceleration.

The second question involves two-dimensional kinematics and Newton's second law. By finding the net force (Fnet) acting on the particle and applying Newton's second law, we can determine the acceleration, and from there use kinematic equations to find the velocity components after a time t. The direction of motion can be obtained by calculating the angle of the velocity vector with respect to the positive x-axis.