An object increases its velocity from 22 m/s to 36 m/s in 5 s. What is the acceleration of the

A major league baseball pitcher throws a pitch that follows these parametric equations: x(t) = 142t y(t) = –16t2 + 5t + 5. The t

azamat

Answer:

(a) $x'(t)= 142$

(b) 142

(c) $y'(t)= -32t+5$

(d) 96.8 mph

(e) 0.426 s

(f) 0.061 rad

Explanation:

Velocity is a time-derivative of position.

(a) $x(t) = 142t$

$x'(t)= 142$

(b) Since $x'(t)= 142$ is independent of $t$ , it follows it was constant throughout. Hence, at any point or time, the horizontal velocity is 142.

(c) $y(t) = - 16t^2+5t+5$

$y'(t)= -32t+5$

(d) When it passes the home plate, the ball has travelled 60.5 ft (from the question). This is horizontal, so it is equivalent to $x(t)$ .

$x(t)= 142t = 60.5$

$t=\dfrac{60.5}{142}= 0.426$ .

In this time, the vertical velocity, $y'(t)$ is

$y(t)= -32\times0.426+5 = -8.632$

The speed of the ball at thus point is $s=\sqrt{142^2+(-8.632)^2}=142$ ft/s

To convert this to mph, we multiply the factor 3600/5280

$s=142\times\dfrac{3600}{5280}=96.8 \text{ mph}$

(e) The time has been determined from (d) above.

$t= 0.426$

(f) This angle is given by

$\theta=\tan^{-1}\dfrac{y'(t)}{x'(t)}$

$\theta=\tan^{-1}\dfrac{-8.632}{142}=\tan^{-1}-0.0607=3.47$ (Note here we are considering the acute angle so we ignore the negative sign)

In radians, this is

$\theta=3.47\times\dfrac{\pi}{180}=0.061 \text{ rad}$

6 0

4 years ago

Which figure represents the electric field lines of two positive point charges?

Naddik [55]

Electric field lines of positive charges are always radially outwards

So here all field lines must have tendency to move out radially as well as two field lines never intersects with each other

So here field lines also do not intersects with each other

So overall the figure C is perfectly representing the field lines of two positive charges as these lines are not intersecting and also originating from two positive charges.

So answer must be

FIGURE C

7 0

3 years ago

A student moves a 1.50 kg book from a shelf 2.00 meters high to a shelf 1.20 meters high.

MAVERICK [17]

Answer:

17.64 j

Explanation:

thats the answer.

6 0

3 years ago

Two Charged spheres of 6.4 nC charge are 16 cm apart. What is the magnitude of the field in middle? ( n = 10^-9, 100 cm = 1 m)

emmainna [20.7K]

Answer:

zero

Explanation:

q = 6.4 nC = 6.4 x 1 0^-9 C

d = 16 cm = 0.16 m

r = 16 / 2 = 8 cm = 0.08 m

Electric field at P due to the charge placed at A

Ea = k q / r^2

Ea = ( 9 x 10^9 x 6.4 x 10^-9) / (0.08 x 0.08) Towards right

Ea = 9000 Towards right

Electric field at P due to the charge placed at B

Eb = k q / r^2

Eb = ( 9 x 10^9 x 6.4 x 10^-9) / (0.08 x 0.08) Towards left

Eb = 9000 Towards left

The magnitude of electric field is same but teh direction is opposite, so the resultant electric field at P is zero.

3 0

3 years ago

Sodium has an atomic mass of 23 and an atomic number of 11, so the

horrorfan [7]

Answer:

12 Neutrons

Explanation:

So the mass of sodium is 22.990. You round it up to get 23(as stated in the problem). So, what exactly is atomic mass?

Atomic Mass is the total amount of neutrons and protons added up to form a total mass. So when you subtract 23-11 you get 12 Neutrons.

Tip: Don't know if you need this but-

The neutrons and protons are typically close in number (unless it's an isotope). So say that you subtract and the numbers of protons and neutrons aren't close at all. Well if that's the case, it's probably wrong.

hope this helps!!

5 0

3 years ago