At the instant a race began, a 89.1 kg sprinter exerted a force of 710 N on the starting block in the direction 110 degrees measured clockwise from the positive x-axis.

(a) What was the horizontal acceleration of the sprinter?

a_x =

(b) If the force was exerted for 0.7 s, what is the velocity of the sprinter?

v_{final} =

a. Fe = 710N.[11o] = Exerted force.

Xe = 710*cos11 = 697.0 N. = Hor.
component of exerted force.
a = Xe/m = 697/89.1 = 7.82 m/s^2.

b. V = Vo + a*t = 0 + 7.82*0.7=5.48 m/s.

NOTE: I used 11o for the given angle,
because 110o is not possible.

To find the horizontal acceleration of the sprinter, we will use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

(a) We are given the force exerted on the starting block, which is 710 N. The direction of this force is 110 degrees measured clockwise from the positive x-axis. Since we want to find the horizontal acceleration, we need to find the horizontal component of the force. To do this, we can use trigonometry.

The horizontal component of the force (F_x) can be calculated using the formula:
F_x = F * cos(theta)

where F is the magnitude of the force and theta is the angle between the force and the positive x-axis.

In this case, F = 710 N and theta = 110 degrees. Plugging in the values, we can calculate the horizontal component of the force:

F_x = 710 N * cos(110 degrees) = -349.25 N

Since the force is in the negative x-direction, the acceleration will also be negative. So, the horizontal acceleration (a_x) of the sprinter is -349.25 N.

(b) To find the velocity of the sprinter, we can use the equation of motion:

v_{final} = v_{initial} + a * t

where v_{initial} is the initial velocity, a is the acceleration, and t is the time.

In this case, the force was exerted for 0.7 s. Since the sprinter is initially at rest, the initial velocity (v_{initial}) is 0. Plugging in the values, we can calculate the final velocity (v_{final}):

v_{final} = 0 + (-349.25 N) * 0.7 s = -244.48 N

The negative sign indicates that the velocity is in the opposite direction of the positive x-axis. So, the velocity of the sprinter is -244.48 m/s.