ok so I have a question

At the instatn a race began, a 57-kg sprinter was found to exert a force of 80 N on the starting lbock at 22 degrees with respect to the ground

what was the horizontal acceleration of the sprinter?

I got roughly 1.3 s^-2 m

ok here's were i need some help

if the force was exerted for .34 s with what speed did the sprinter eave the starting block?

ok didn't he leave the starting block with an intial speed of zero?

by definition of accleration
a=t^-1 (V-Vo)

if theh Vo is not considered to be zero how to find the V and the Vo to fidn the acceleration

maybe there's another way to do this i do not know how to find the intial speed from the starting block

80 cos 22 = 74.2

a = F/m = 74.2/57 = 1.3 m/s^2 agree

he leaves the block not at t =0 but at t=.34 s
v = Vo + a t
v = 0 + 1.3 (.34) = .442 m/s

ok thanks

To find the horizontal acceleration of the sprinter, you can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the net force on the sprinter is the force exerted on the starting block.

The horizontal component of the force exerted on the starting block can be found using the formula:

F_horizontal = F * cos(theta),

where F is the force exerted on the starting block and theta is the angle between the force and the ground.

Plugging in the values given in the question:

F_horizontal = 80 N * cos(22 degrees).

Now, using Newton's second law:

F_horizontal = m * a,

where m is the mass of the sprinter and a is the horizontal acceleration we want to find.

Solving for a:

a = F_horizontal / m.

Plugging in the values:

a = (80 N * cos(22 degrees)) / 57 kg.

Evaluating this expression gives you the horizontal acceleration of the sprinter.

Now, to find the initial speed of the sprinter, we need to use the relationship between acceleration, time, initial velocity, and final velocity:

a = (V - Vo) / t,

where a is the acceleration, V is the final velocity, Vo is the initial velocity, and t is the time.

In this case, the sprinter starts from rest, so the initial velocity (Vo) is zero. Rearranging the equation:

V = a * t.

Plugging in the values:

V = (horizontal acceleration) * 0.34 s.

Evaluating this expression will give you the speed at which the sprinter left the starting block.