C

1003148602

Level: 
C
Consider an object thrown at an angle of \( 30^{\circ} \) above the horizontal with the initial velocity of \( 40\frac{\mathrm{m}}{\mathrm{s}} \). How long does it take for the object to reach its maximum height? \[ \] Note: The height \( y \) of an object thrown is described by the formula \( y=v_0t\sin\alpha-\frac12gt^2 \), where \( v_0 \) is the initial velocity, \( g \) is gravitational acceleration (count with the rounded value \( 10\frac{\mathrm{m}}{\mathrm{s}^2}\)), \( t \) is the time period of the object motion in seconds, and \( \alpha \) is the angle to the horizontal at which the object is thrown.
\( 2\,\mathrm{s} \)
\( 4\,\mathrm{s} \)
\( 8\,\mathrm{s} \)
\( 1\,\mathrm{s} \)

1003148601

Level: 
C
Consider an object thrown upwards from the ground with the initial velocity of \( 30\frac{\mathrm{m}}{\mathrm{s}} \). The object moves upwards with decreasing vertical velocity until it stops. Then it starts moving vertically downwards. Find the greatest height above the ground the object does reach. \[ \] Note: The vertical distance \( y \) of a thrown object is described by the equation \( y=v_0t-\frac12gt^2 \), where \( v_0 \) is the initial velocity of the thrown object, \( g \) is gravitational acceleration (count with the rounded value \( 10\frac{\mathrm{m}}{\mathrm{s}^2}\)), and \( t \) is the time period of the object motion in seconds.
\( 45\,\mathrm{m} \)
\( 135\,\mathrm{m} \)
\( 360\,\mathrm{m} \)
\( 40\,\mathrm{m} \)

1003177803

Level: 
C
Choose the domain of the expression. \[ \frac1{\sqrt{|3x-9|-\sqrt2}} \]
\( \left(-\infty;3-\frac{\sqrt2}3\right)\cup\left(3+\frac{\sqrt2}3;\infty\right) \)
\( \left(-\infty;-3-\frac{\sqrt2}3\right)\cup\left(3+\frac{\sqrt2}3;\infty\right) \)
\( \left(-\infty;-3+\frac{\sqrt2}3\right)\cup\left(3+\frac{\sqrt2}3;\infty\right) \)
\( \left(-\infty;-3-\frac{\sqrt2}3\right)\cup\left(-3+\frac{\sqrt2}3;\infty\right) \)

1003158902

Level: 
C
The length of a rectangle is \( 4\,\mathrm{cm} \) and width is \( x\,\mathrm{cm} \). The rectangle is divided by vertical crossing line into two parts so that one part is a square with the side of \( x\,\mathrm{cm} \) (see the picture). What is the maximum area of the remaining part of the rectangle?
\( 4\,\mathrm{cm}^2 \)
\( 2\,\mathrm{cm}^2 \)
\( 16\,\mathrm{cm}^2 \)
\( 1\,\mathrm{cm}^2 \)

1003158901

Level: 
C
An object is moving with a constant deceleration in a straight line. Displacement \( s \) (in metres) in time \( t \) (in seconds) is modelled by \( s=24t-3t^2 \). Find the displacement of the object from the moment it starts to decelerate until it stops.
\( 48\,\mathrm{m} \)
\( 144\,\mathrm{m} \)
\( 16\,\mathrm{m} \)
\( 96\,\mathrm{m} \)