7. Die grosse Rolltreppe im Einkaufszentrum ist 28.8 m lang und bewegt sIch mit \( 1.6 \mathrm{~m} / \mathrm{s} \). Maria rennt aber lieber mit \( 2.4 \mathrm{~m} / \mathrm{s} \) die Treppe hoch, die parallel dazu verläuft. Ihr Bruder Remo nimmt die Rolltreppe. a) Wie viele Sekunden Vorsprung muss sie Remo lassen, damit sie gleichzeitig oben ankommen? b) Wie schnell wäre sie oben, wenn sie die Rolltreppe hochrennen würde?

हल दिया है-गेंद का प्रारम्भिक वेग \( 20 \mathrm{~cm} \mathrm{~s}^{-1} \) है। मेज के द्वारा गेंद पर घर्षण बल लगने के कारण गेंद का वेग 10 s में शून्य हो जाता है। वेग-समय ग्राफ एक सरल रेखा है जिससे यह पता चलता है कि गेंद एक नियत त्वरित बल के साथ चलती है।

Una palla di massa \( m_{1}=24 \mathrm{~g} \), che viaggia alla velocità \( v_{1} \), urta elasticamente una palla ferma di massa \( m_{2}=\frac{1}{2} m_{1} \). Dopo l'urto, la seconda palla va a colpire elasticamente una terza palla ferma, di massa \( m_{3} \). Tutti gli urti avven- gono lungo la stessa retta. Quale deve essere la massa \( m_{3} \) affinché la sua velocita dopo l'urto sia uguale a \( v_{1} \) ?

(a) 8 (b) \( 8 \sqrt{2} \quad(c) 8 \sqrt{3} \quad(d) 12 \) (49) A uniform rod \( \overline{A B} \) of length 6 meters and weight \( 8 \mathrm{~kg} \cdot \mathrm{wt} \). is attached to a hinge fixed in a vertical wall at its end A the rod is kept horizontal by attaching it at a point C on the rod (where \( A C=4 \) meters) by a string which its other end is fixed at the point D on the wall above A exactly and at a distance 4 meters from it. Calculate the magnitude of the tension in the string and the reaction of the hinge.

EXERCISES It is known that the flow of fluid \( (\mathrm{Q} \) rate) is a fluid volume passing per unit time, based on the pressure gradient \( (\mathrm{P} / \ell) \) where \( (p) \) is the pressure between the ends of the tube flow stream, \( (\ell) \) is the length of pipe flow, also depends on the viscosity of the liquid \( (\eta) \) and the radius of the tube \( (r) \), by using the concept of compatibility between the units and dimensions theory derive a mathematical formula for flow rate depending on the variables mentioned above.

Train moving with speed of \( (40 \mathrm{~m} / \mathrm{s}) \) the driver have resorted to the use of brakes to reduce the speed of the train movement by rate \( \left(-2 \mathrm{~m} / \mathrm{s}^{2}\right) \) Calculate: a) The amount of time it takes for the train even stops completely. b) The amount of distance traveled since the train began braking until it stops